WO2021227012A1 - 一种姿态测量方法 - Google Patents

一种姿态测量方法 Download PDF

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Publication number
WO2021227012A1
WO2021227012A1 PCT/CN2020/090520 CN2020090520W WO2021227012A1 WO 2021227012 A1 WO2021227012 A1 WO 2021227012A1 CN 2020090520 W CN2020090520 W CN 2020090520W WO 2021227012 A1 WO2021227012 A1 WO 2021227012A1
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Prior art keywords
measurement
attitude
alignment
gyroscope
update
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PCT/CN2020/090520
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English (en)
French (fr)
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薛旭
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中国科学院地质与地球物理研究所
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Priority to EP20838867.8A priority Critical patent/EP3933166A4/en
Priority to US17/248,896 priority patent/US11187535B1/en
Publication of WO2021227012A1 publication Critical patent/WO2021227012A1/zh

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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B47/00—Survey of boreholes or wells
    • E21B47/02—Determining slope or direction
    • E21B47/022—Determining slope or direction of the borehole, e.g. using geomagnetism
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
    • G01C19/56—Turn-sensitive devices using vibrating masses, e.g. vibratory angular rate sensors based on Coriolis forces
    • G01C19/567—Turn-sensitive devices using vibrating masses, e.g. vibratory angular rate sensors based on Coriolis forces using the phase shift of a vibration node or antinode
    • G01C19/5691—Turn-sensitive devices using vibrating masses, e.g. vibratory angular rate sensors based on Coriolis forces using the phase shift of a vibration node or antinode of essentially three-dimensional vibrators, e.g. wine glass-type vibrators
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/183—Compensation of inertial measurements, e.g. for temperature effects
    • G01C21/188—Compensation of inertial measurements, e.g. for temperature effects for accumulated errors, e.g. by coupling inertial systems with absolute positioning systems

Definitions

  • the invention relates to the technical field of directional drilling attitude measurement, in particular to an attitude measurement method for large inclined wells and horizontal wells, and a directional drilling gyro measurement-while-drilling method.
  • gyroscopes that can meet high temperature, strong vibration, small size and high precision have always been the persistent pursuit of inertial technology in the petroleum industry, especially for the magnetic flux during directional drilling.
  • door interference it is not that a gyroscope is currently needed, but there is no suitable gyroscope product that can work normally for a long time under harsh environments such as high temperature and strong vibration.
  • a gyro-related technology for steering drilling applications reliability in harsh environments is an important basis for selection. Therefore, it is necessary to develop a method that can meet the most demanding use scenarios in the field of oil drilling measurement, and environmental adaptability under high temperature and strong vibration environments Problems, zero-bias repeatability problems, etc.
  • the existing calibration method only starts from the differences in the suppression ability of external environmental interference and the amount of calculation, and does not consider the specific use environment of the GMD, that is, the harsh environment such as high temperature and strong vibration, which causes greater damage to the inertial instrument. Drift error.
  • the actual drift error of the inertial instrument will affect the calibration accuracy of the existing calibration method. Under the working conditions of high temperature, strong vibration and harsh environment, the zero offset repeatability error is the main bottleneck restricting the accuracy of the gyroscope.
  • the present invention provides an attitude measurement method, which has fault tolerance and the ability to align under small shaking, and can improve the observability of inertial instrument errors without changing the accuracy of the inertial instrument itself, and suppress the gyro from time to time. Start-up repeatability error, thereby improving the accuracy of attitude measurement.
  • the present invention provides an attitude measurement method used in a strapdown inertial navigation system, characterized in that a method of performing fine alignment at multiple positions respectively is used to suppress the repetitive drift of the gyroscope;
  • the steps of the method include:
  • the strapdown inertial navigation system is indexed to the nth position, and the attitude and speed are updated according to the result of the n-1th fine alignment during the indexing process;
  • an implementation manner is further provided, and the content of the precise alignment using the Kalman algorithm includes: time update and/or measurement update;
  • Time update complete the update of state variables according to the real-time data collected by the system, including attitude update and speed update;
  • the measurement update, the measurement data corrects the error of the status update, and realizes the optimal estimation
  • Kalman filter uses zero-speed correction speed measurement and the earth rotation angular rate constraint angular rate measurement for measurement update and optimal estimation to improve alignment accuracy.
  • the data of the fine alignment initial value includes: well inclination angle, tool face angle, and azimuth angle .
  • the measurement update step includes:
  • step 1) Determine whether the measured data value is valid, if it is valid, go to step 2), otherwise, do not update, and use the time update result as the final result of Kalman filtering;
  • an implementation manner is further provided, and judging whether the measured data value is valid is achieved by judging whether the drill collar is in a static state and/or judging whether the external disturbance meets the alignment requirements; if If the drill collar is in a static state and/or the external disturbance meets the alignment requirements, the measured data value is judged to be valid, otherwise the measured data value is judged to be invalid.
  • the above aspects and any possible implementation manners further provide an implementation manner.
  • the determination of whether the drill collar is in a static state is specifically: determining whether the sensitive velocity observation and/or the sensitive angular rate observation is less than the determination threshold, if so, It is determined that the drill collar is in a static state, otherwise it is not in a static state.
  • the above aspects and any possible implementation manners further provide an implementation manner.
  • the determination of whether the external disturbance meets the alignment requirements is specifically: determining whether the disturbance amount of the external mud or the vibration amount sensed by the vibration sensor is less than the set value Threshold; if it is, it is determined that the external disturbance meets the alignment requirements, otherwise it does not;
  • the specific values of the thresholds in the above-mentioned judgment conditions are determined according to the actual conditions such as the drilling geological environment and the depth.
  • the sensitive velocity observation is the real-time acceleration value of the gyroscope;
  • the sensitive angular rate observation is the root mean square value of the gyroscope's angular rate.
  • step 2) includes: according to the sequential processing method, respectively solving the velocity measurement Z v corrected by the zero velocity and the rotation angle of the earth
  • the rate-constrained angular rate measurement Z ⁇ is composed of the measurement equation, which realizes the optimal estimation of the constant drift error of the X and Y horizontal gyroscopes and the constant drift error estimation of the Z-axis gyroscopes, and finally completes the estimation of the attitude and azimuth misalignment angles. Excellent estimate.
  • the above aspect and any possible implementation manner further provide an implementation manner, which completes the one-step prediction of the state and the one-step prediction of the mean square error when the time is updated.
  • the measurement method further includes a rough alignment at the first position, and the first initial value is the result of the rough alignment. Time fine alignment.
  • ⁇ v n is the velocity error
  • ⁇ n is the misalignment angle of the strapdown inertial navigation math platform
  • Is the constant drift of the gyro Is the constant zero offset of the accelerometer
  • ⁇ ie is the rotation rate of the earth
  • L is the latitude
  • T represents the transposition of the matrix
  • attitude transfer matrix between the navigation coordinate system and the carrier coordinate system Specifically:
  • ⁇ is the pitch angle
  • ⁇ is the heading angle
  • ⁇ is the roll angle
  • V v is the speed measurement noise in the navigation coordinate system
  • V ⁇ refers to the angular rate measurement noise
  • v n is the output speed
  • ⁇ v n is the velocity error
  • ⁇ v n is used as the measurement data
  • I is the unit matrix
  • Z ⁇ is the angular rate observation
  • Z ⁇ is the velocity observation.
  • the above aspects and any possible implementation manners further provide an implementation manner in which the Euler analysis method is used to perform rough alignment of the static base, and the calculation is directly performed based on the data of the accelerometer and the gyroscope.
  • the above aspects and any possible implementation manners further provide an implementation manner.
  • the first Kalman alignment and the second Kalman alignment use both within 130s, and the horizontal well position alignment can be achieved.
  • the precision is within 1deg.
  • the present invention provides a measurement-while-drilling system.
  • the system includes a strapdown inertial navigation system.
  • the strapdown inertial navigation system includes a three-axis gyroscope and a three-axis accelerometer;
  • the described attitude measurement method suppresses the repetitive drift error of the gyroscope, and improves the accuracy of the measurement while drilling of the directional drilling.
  • the gyroscope is a Coriolis vibration gyroscope.
  • the gyroscope is a high-temperature resonant gyroscope
  • the strapdown inertial navigation system further includes a shock absorber, and the shock absorber is fixedly connected with the high temperature resonant gyroscope.
  • the high-temperature resonant gyroscope includes a resonator, a circuit board, a piezoelectric ceramic, a supporting base, a housing, and a terminal.
  • the sub is placed in the housing and connected to the support base, the piezoelectric ceramic is connected to the terminal through a conductive metal wire, the circuit board realizes signal transmission, and is fixed at the key process points of the internal components of the gyroscope;
  • the key process points of the connection are between the piezoelectric ceramic and the resonator, between the terminal and the piezoelectric ceramic, between the terminal and the circuit board, between the support base and the resonator, and between the housing and the support base.
  • the present invention provides a continuous navigation measurement system, the system includes a strapdown inertial navigation system, and the strapdown inertial navigation system includes a three-axis gyroscope and a three-axis accelerometer;
  • the described attitude measurement method suppresses the repetitive drift error of the gyroscope and improves the attitude measurement accuracy in the navigation process.
  • Attitude measurement information includes horizontal attitude angle and azimuth angle, which are three parameters: usually, pitch angle (well inclination angle) and roll angle (tool face angle) are called horizontal attitude, and heading angle (alignment azimuth) is called horizontal attitude. It is the azimuth angle.
  • the purpose of the initial alignment is to collect the accelerometer and gyroscope data in real time and perform related algorithm processing to obtain the attitude information (horizontal attitude angle and azimuth angle) of the carrier.
  • the present invention can obtain the following technical effects: the alignment method of the present invention can still find the north normally when the interference angular rate caused by mud sloshing is greater than the rotation angular rate of the earth, and has better fault tolerance and small size.
  • the ability to align under shaking can improve the observability of the inertial instrument error without changing the accuracy of the inertial instrument itself, and realize the optimal estimation of the inertial instrument error, thereby improving the initial alignment accuracy; based on the Kalman optimal estimation
  • the dual position alignment algorithm uses strapdown inertial navigation attitude update algorithm and speed update algorithm to update the angular motion and linear motion of the carrier in real time, and adopts zero-speed and/or earth rotation angular rate correction algorithm for measurement update and optimal estimation , It makes the optimal estimation accuracy irrelevant to the accuracy of indexing, and there is no need to know the exact position of the indexing mechanism. This is very beneficial in engineering practice, avoiding the design of complex stop structures, and avoiding the use of high-temperature measurement Angle mechanism; rotation position eliminates drift error or drift measurement.
  • FIG. 1 is a schematic diagram of a single-axis gyroscope rotation position elimination zero offset principle diagram provided by an embodiment of the present invention
  • Fig. 2 is a curve diagram of misalignment angle of north-south strike well trajectory alignment during dual-position alignment (ie indexed alignment) provided by an embodiment of the present invention
  • Figure 3(a) is a graph of the gyroscope constant drift estimation error curve of the north-south-strike well trajectory during the deviation correction provided by the indexing method according to an embodiment of the present invention
  • Figure 3(b) is a curve diagram of the constant drift estimation error of the accelerometer of the north-south well trajectory during the deviation correction provided by the indexing method according to an embodiment of the present invention
  • Fig. 5(a) is a graph of the gyroscope constant drift estimation error curve of the east-west well trajectory during the deviation correction provided by the indexing method according to an embodiment of the present invention
  • Figure 5(b) is a curve diagram of the constant drift estimation error curve of the accelerometer of the east-west well trajectory during the correction of the deviation provided by the indexing method according to an embodiment of the present invention
  • Fig. 6 is a graph showing the accuracy of azimuth alignment of a full well inclination obtained under different constant drift errors of the dual-position correction method provided by an embodiment of the present invention
  • FIG. 7 is a flowchart of a two-position Kalman filter algorithm provided by an embodiment of the present invention.
  • FIG. 8 is a flowchart of a sequential processing method of a two-position Kalman algorithm according to an embodiment of the present invention.
  • FIG. 9 is a schematic diagram of a dual position + Kalman alignment process provided by an embodiment of the present invention.
  • Fig. 10 is a curve diagram of the misalignment angle error of the north-south strike well trajectory during the correction of the deviation by the dual position + Kalman alignment method according to an embodiment of the present invention
  • Fig. 11(a) is a diagram of the gyroscope drift estimation error of the north-south strike well trajectory when the dual position + Kalman alignment method is provided in an embodiment of the present invention
  • Figure 11(b) is a diagram of the gyroscope drift estimation error of the north-south strike well trajectory when the dual position + Kalman alignment method is provided in an embodiment of the present invention
  • FIG. 12 is a graph of the misalignment angle error curve of a vertical well when the dual position + Kalman alignment method is provided in an embodiment of the present invention.
  • Figure 13(a) is a graph of the drift estimation error curve of the vertical well gyroscope when the dual position + Kalman alignment method is provided in an embodiment of the present invention
  • FIG. 13(b) is a graph of the drift estimation error curve of the vertical well accelerometer when the dual position + Kalman alignment method is provided in an embodiment of the present invention
  • Figure 14(a) is a curve diagram of the estimation error of the small well deviation misalignment angle of the east-west well trajectory during the correction of the deviation by the dual position + Kalman alignment method provided by an embodiment of the present invention
  • Figure 14(b) is a curve diagram of the estimation error of the large deviation angle of the east-west well trajectory during the correction of the deviation by the dual position + Kalman alignment method provided by an embodiment of the present invention
  • Figure 15(a) is a diagram of the constant drift estimation error of the gyroscope under the 70° deviation angle of the east-west well trajectory when the dual position + Kalman alignment method is provided in an embodiment of the present invention
  • Figure 15(b) is a diagram of the constant drift estimation error of the accelerometer under the 70° deviation angle of the east-west well trajectory when the dual position + Kalman alignment method is provided in an embodiment of the present invention
  • Fig. 16 is a simulation curve diagram of GMD alignment misalignment angle error when the east-west well trajectory is full inclination angle when the dual position + Kalman alignment method is provided in an embodiment of the present invention
  • Fig. 17(a) is a graph showing the estimation error curve of the constant drift of the gyroscope under the full inclination angle of the east-west well trajectory when the double position + Kalman alignment method is provided in an embodiment of the present invention
  • Figure 17(b) is a curve diagram of the constant drift estimation error curve of the accelerometer under the full deviation angle of the east-west well trajectory when the dual position + Kalman alignment method is provided in an embodiment of the present invention
  • Figure 18 is a schematic diagram of the attitude measurement of a standard strapdown inertial navigation system
  • Fig. 19 is a schematic diagram of the steering drilling provided by the present invention: a horizontal well.
  • a horizontal well includes: vertical (well) section, target displacement (inclined well section), and horizontal (well) section.
  • the inclination angle of the vertical section is defined as 0°
  • the target displacement ( Deviated well section) refers to the section where the well inclination angle is greater than 0° to 90°. It is usually divided into small well inclination angles (such as 0°-20°) and large well inclination angles (such as greater than 70°). There is no clear definition.
  • the horizontal section refers to the section where the inclination angle is 90°.
  • the definition of total well inclination means that it covers the vertical section to the horizontal section, and the inclination angle ranges from 0° to 90°.
  • Dual position is one of the implementation schemes, and practically any position can be used. From the perspective of mechanical structure design, dual-position alignment facilitates mechanical structure design, that is, through the design of mechanical stops, accurate two-point positioning can be achieved.
  • the reasoning logic of the measurement method of the present invention is as follows:
  • Gyro guidance is based on the principle of gyrocompass (Gyrocompass), which mainly uses inertial devices (accelerometers and gyroscopes) to measure the earth's rotation angular rate vector and gravitational acceleration vector, so as to calculate the angle between the carrier and the geographic north.
  • Gyrocompass mainly uses inertial devices (accelerometers and gyroscopes) to measure the earth's rotation angular rate vector and gravitational acceleration vector, so as to calculate the angle between the carrier and the geographic north.
  • the rotation angular rate of the earth ⁇ ie is a fixed value of 15.041067°/h (about 0.0042°/s), and the longitude and latitude of the measured carrier are ⁇ and L respectively, using the "Northeast Sky" geographic coordinate system.
  • the horizontal component of the earth's rotation angular rate is ⁇ N , and its magnitude depends on the latitude L of the measurement location.
  • the horizontal component of the earth's rotation is about 11.52°/h. The higher the latitude, the smaller the horizontal component, and the horizontal component tends to zero near the pole.
  • the output value of the gyroscope is obtained:
  • ⁇ ob is the output value of the gyroscope, that is, the observation value, and B is the zero bias of the gyroscope.
  • the azimuth angle ⁇ of the carrier can be calculated.
  • the measurement data of the gyroscope includes the bias B of the gyroscope itself, and its value will directly affect the calculation of the azimuth angle. As a result, it is usually eliminated by means of multi-point indexing or continuous rotation modulation.
  • Figure 1 shows the working principle of a single-axis gyroscope changing its sensitive direction through the rotation of the indexing mechanism. In order to facilitate the mechanical design of the indexing mechanism, a simple 0 is used. °, 180° two position indexing methods, the output of the gyroscope are:
  • SF 1 , SF 2 , U 1 , U 2 , B 1 , B 2 refer to the scale factor and output (analog or Digital value) and zero offset.
  • ⁇ B is the residual drift error after indexing compensation. Taking Taylor expansion of the above formula and ignoring high-order terms, the estimated error (accuracy) at two positions is obtained as
  • Equation (1.7) gives the basic formula for the estimation accuracy error of the gyroscope north-seeking. It can be seen that the north-seeking accuracy of the two-position indexing is related to the residual drift error of the gyroscope and the local latitude.
  • the guiding principle adopts the Euler angle analysis method, and the Euler angle analysis method uses the gyroscope and accelerometer information to directly obtain the carrier’s pitch angle (inclination angle) ⁇ , roll angle (tool surface) ⁇ and heading angle (azimuth angle) ⁇
  • the Euler angle analysis method is used to give the principle and accuracy limit of the coarse alignment.
  • g, ⁇ ie , L respectively represent the magnitude of local gravitational acceleration, the magnitude of the angular velocity of the earth's rotation, and the local latitude.
  • ⁇ N ⁇ ie cosL
  • ⁇ U ⁇ ie sinL.
  • the gyroscope and accelerometer in the GMD system measure the projection of the gravity vector and the angular velocity of the earth’s rotation under the carrier system, respectively. The influence of mud sloshing interference is ignored.
  • the measurement data of component acceleration is:
  • the rough alignment time is generally very short.
  • the measured data value of the inertial meter is generally a smooth average value over a period of time.
  • the longer the smoothing time the better the accuracy can be obtained.
  • the length of the smoothing time can be judged and analyzed by the Allan variance test data. The optimal time for smoothing is selected based on the time when the Allan variance "bottoms out”.
  • Equations (2.4), (2.5), (2.7) constitute the basic algorithm of Euler angle coarse alignment. The following analyzes the ultimate accuracy of Euler's analytical method for alignment on static base.
  • Equations (2.9), (2.10) and (2.11) determine the limit accuracy of the static base alignment, that is, the formula of the analytical method for coarse alignment, which can be directly calculated through the accelerometer and gyroscope data.
  • the attitude alignment accuracy under static base conditions mainly depends on the drift error of the east and north accelerometers, while the azimuth alignment accuracy mainly depends on the drift error of the east gyro and the east accelerometer.
  • the superscript ⁇ represents the estimated value, or the calculated value, and the value without it represents the state value.
  • the estimated value of the inclination angle ⁇ is
  • the measured data values of the accelerometer and gyroscope selected in equations (2.4), (2.5), (2.7) can be in many ways.
  • the average value of the sampling value over a period of time, the sampling time and the limit accuracy are selected. It is usually expressed by the method of Allan variance, and the lowest point of Allan variance is used as the evaluation of the accuracy limit. Therefore, the longer the integration time, the higher the smoothing accuracy, but for the presence of trend error or drift error, the integration time The length depends on the time constant of the drift error.
  • the traditional method to eliminate drift errors and improve the accuracy of azimuth alignment is to use the index of rotation position.
  • the IMU is rotated in one direction to construct the attitude transfer matrix at two positions, increasing the constant value zero Partial observability.
  • the design of the indexing mechanism can only be around the axis of the probe, that is, around the direction of the input axis of the Z-axis gyroscope.
  • the positions before and after the gyroscope indexing are b 1 and b 2 , and the sample output average values of the corresponding gyroscope during the alignment time are respectively Record the average value of the sampled output before and after the accelerometer indexing is as follows: with Assuming that the angle between the positions of b 1 and b 2 is ⁇ , the resulting state transition matrix is
  • Equation (3.2) gives the horizontal gyro output at position b 2 as:
  • the output of the horizontal accelerometer at position b 2 can also be obtained as:
  • the estimated zero offset of the horizontal accelerometer is:
  • the estimated value of the accelerometer after dual-position calibration is:
  • the estimated value of the gyroscope after two-position calibration is:
  • the accelerometer and gyroscope on the Z-axis are not observable, and the average value before and after the index is directly taken as the estimated value after calibration:
  • the calibrated inclination angle can be obtained as:
  • the tool face angle after calibration is:
  • the azimuth angle after calibration is:
  • Equations (3.7) ⁇ (3.9) constitute the basic algorithm for resolving dual position alignment with 180° rotation around the Z axis.
  • the analytical dual position solves the problem of calibration of the constant drift error of the inertial instrument, and improves the alignment accuracy, especially the azimuth alignment accuracy.
  • the main alignment error comes from the error of the indexing mechanism and the random drift of the inertial instrument Error, due to the 0-180° indexing design, it only pays attention to the final indexing positioning accuracy, which facilitates the design of the indexing mechanism.
  • the indexing and positioning accuracy can be improved through the design of the stop structure, which simplifies the design;
  • the quartz flexible accelerometer has a random error mean square value of 20 ⁇ g in the frequency band of 100Hz.
  • the latitude 40°N can be set to obtain the random error band
  • the azimuth error is about 0.1deg. In the following simulation, a similar conclusion will be drawn.
  • the error parameters of the gyroscope and accelerometer are shown in Table 1 for the high-temperature inertial instrument simulation parameter settings.
  • the initial position is set to [116°E, 40°N, 100m]
  • the first alignment position is in the first 145s.
  • Simulation 1 The well trajectory is north-south, the vertical well attitude azimuth [0°,0°,0°] in the geographic coordinate system, and the horizontal well attitude azimuth is [90°,0°,0°].
  • Figure 2 is the right Accurate misalignment angle error curve, Fig. 3(a) and Fig. 3(b) successively show the constant drift estimation error of the gyroscope and accelerometer.
  • the azimuth alignment accuracy is not affected by the inclination angle, that is, from the vertical section to the horizontal section, the azimuth measurement error is always around 0.1° , This is also in line with the conclusion of formula (2.11), and the mechanism of initial alignment is not difficult to understand.
  • the azimuth misalignment angle is related to the accuracy of the equivalent eastward gyro.
  • the east-facing gyroscope can always be modulated by indexing, that is, the constant drift of the east-west gyroscope is always observable, that is, the constant value of the equivalent east-facing gyroscope can be eliminated at any inclination angle through indexing. drift.
  • the final azimuth alignment accuracy mainly depends on the random drift of the east-facing gyroscope.
  • the simulation results in Fig. 2 can verify this conclusion.
  • the estimated error curve of the east misalignment angle in Fig. 2 and the Z-axis accelerometer in Fig. 3(b) shows that as the inclination angle increases, the observability of the Z-axis accelerometer becomes worse.
  • the east-direction misalignment angle error increases with the increase of the inclination angle, but the error is much smaller than the target accuracy index, and this effect can be ignored.
  • Simulation 2 The well trajectory is east-west. In the geographic coordinate system, the vertical well attitude coordinates are [0°,0°,90°], and the horizontal well attitude coordinates are [90°,0°,90°]. The simulation results are shown in Figure 4.
  • the azimuth measurement accuracy at large tilt angles can be improved by reducing the constant drift of the gyroscope.
  • Figure 6 shows the azimuth measurement accuracy simulation curves of the gyroscope with different constant drifts at different tilt angles.
  • the constant drift of the gyroscope is required to be less than 0.2deg/h, and for working conditions under high temperature, strong vibration and harsh environment ,
  • the zero offset repeatability error is the main bottleneck restricting the accuracy of the gyroscope. It is very challenging to develop a gyroscope that meets the 0.2deg/h constant drift error under the operating conditions.
  • the inclination angle of the small well under the east-west trajectory and the north-south strike trajectory of the full well inclination angle (0° ⁇ 90°) can be effectively improved.
  • the azimuth accuracy, but the azimuth accuracy of the east-west traces under large well inclination angles still cannot meet the requirements of use, so we wait for a more effective method to improve the azimuth measurement of large well inclination angles when the accuracy of inertial devices is limited. Accuracy.
  • the invention adopts a multi-position+Kalman alignment method to solve the drift measurement problem of the east-facing gyroscope at a large inclination angle.
  • the content of this method includes:
  • the navigation coordinate system is taken as the northeast sky geographic coordinate system, and a 12-dimensional inertial navigation system precision alignment mathematical model is established.
  • the state variables of the Kalman filter are:
  • g is the acceleration due to gravity
  • f n [0 0 g]
  • ⁇ is defined as the antisymmetric matrix formula
  • H [a b c]
  • antisymmetric matrix is defined as
  • V v is the speed measurement noise in the navigation coordinate system
  • ⁇ v n is the speed error
  • I is the identity matrix
  • X is the Kalman filter state variable
  • Z ⁇ is the speed observation
  • H v [I 3 ⁇ 3 0 3 ⁇ 3 0 3 ⁇ 3 0 3 ⁇ 3 0 3 ⁇ 3 ].
  • the theoretical analysis of observability of single-position Kalman alignment is relatively mature.
  • the Kalman optimal estimation alignment method under static base is adopted.
  • the observability of ⁇ U , ⁇ N , and ⁇ U is weak, and And ⁇ E are completely unobservable.
  • Kalman alignment on a single-position static base cannot estimate the constant drift of the east and north accelerometers and the error of the east gyroscope.
  • the error of the east accelerometer determines the north misalignment angle
  • the error of the north accelerometer determines the east direction.
  • the misalignment angle and the azimuth misalignment angle mainly depend on the equivalent east gyro error. Therefore, under the condition of a static base, the single-position Kalman optimal estimation method of initial alignment is used.
  • the accuracy of the current high-temperature quartz flexible accelerometer can basically meet the accuracy requirements of attitude alignment under a static base.
  • the accuracy of the gyroscope, especially the repeatability error of successive starts, has become the core of restricting the accuracy of azimuth alignment. factor.
  • the dual-position alignment method essentially belongs to the initial alignment of Euler angles on a static base.
  • the analytical dual-position alignment cannot achieve the optimal estimation of the inertial instrument error, especially under the east-west well trajectory. It can be seen from Fig. 4 that when When the inclination angle is greater than 10°, the accuracy of azimuth alignment deteriorates sharply.
  • the analytical method only picks up the output information of the inertial instrument on the carrier for a period of time as the observation, its alignment accuracy is limited by the ideal degree of the carrier’s static and no shaking during the sampling period. In the north state, the mud motor may still be working.
  • the Kalman multi-position alignment based on the best estimate has the ability to tolerate information errors, and has the ability to align under small shaking, and can improve the observability of inertial instrument errors without changing the accuracy of the inertial instrument itself.
  • the optimal estimation of the inertial instrument error is realized, thereby improving the initial alignment accuracy.
  • two-position indexing around the axial direction of the probe tube is the preferred solution of the present invention.
  • equation (4.2) Similar to the state equation established for the initial alignment of the Kalman optimal estimation under a static base, the state equation of the two-position Kalman optimal estimation is shown in equation (4.2). Assuming that the indexing time is very short, the constant drift error is considered It is fixed before and after the indexing, similar to the dual position analytical method alignment, and the attitude matrix of the inertial navigation system is changed through external rotation. This increases the observability of the system state variables, especially the constant drift of the inertial instrument. The dual-position method realizes fine alignment while also estimating the error of the inertial instrument. Similarly, when the angle of rotation is 180°, the attitude matrix The amount of change of is the largest, and the observability of the estimated state is the strongest. Solving equations (4.5) and (4.6),
  • the X-axis gyroscope and Y-axis gyroscope can be separated by indexing Repeatability error.
  • the Z-axis gyroscope will become an east-facing (west-facing) gyroscope.
  • the indexing mechanism can only be around the Z-axis. Therefore, the large inclination angle Next, the Z-axis gyroscope will not be able to separate the error coefficient by rotating the position.
  • V ⁇ refers to the angular rate measurement noise
  • Z ⁇ refers to the angular rate measurement
  • the output model of the gyro in the carrier coordinate system can be expressed as:
  • ⁇ b is the real angular rate input value of the gyroscope
  • ⁇ 0 is the constant drift of the gyroscope
  • ⁇ r is the slow-varying drift
  • ⁇ w is the fast-varying drift
  • ⁇ 0 is mainly the repeatability error of successive start-ups, which can be expressed by random constants.
  • the error model is:
  • the slow-varying drift ⁇ r represents the trend term of the gyroscope and represents the rate ramp term in the Allan variance. It can usually be described by a first-order Markov process, namely:
  • ⁇ g is the correlation time of the Markov process
  • w r is white noise
  • the output model of the gyroscope can be simplified as:
  • the zero bias error of the gyroscope is:
  • the angle random walk coefficient ARW is usually used to represent the term ⁇ w related to white noise.
  • the accelerometer output model can be simplified to:
  • the average value of the accelerometer sampling output, f b is the true acceleration value of the accelerometer, Is the constant drift of the accelerometer, It is the random error of white noise.
  • X k is the 12 ⁇ 1 dimensional state vector shown in formula (4.1) (in formula (4.1): velocity error ⁇ v n , strapdown inertial navigation math platform misalignment angle ⁇ n , high temperature Gyro constant drift And high temperature accelerometer constant value zero deviation
  • Z k is a measurement vector composed of velocity measurement Z v and angular rate measurement Z ⁇
  • ⁇ k/k-1 is a 12 ⁇ 1 dimensional state
  • k-1 is the previous moment
  • k is the one-step recursive moment of k-1
  • ⁇ k/k-1 is the system noise allocation matrix
  • H k is the measurement matrix
  • W k-1 is the system noise vector
  • V k is the measurement noise vector, including velocity measurement noise and angular rate measurement noise
  • W k-1 and V k are uncorrelated zero mean values
  • the sequence of Gaussian white noise vectors has:
  • Q k and R k are respectively called the variance matrix of system noise and measurement noise. In Kalman filtering, they are required to be known non-negative definite matrix and positive definite matrix respectively.
  • Figure 7 is a flowchart of the Kalman filter algorithm. It can be seen from the figure that the algorithm flow of Kalman filter can be divided into two calculation loops and two update processes. The left side is the filter calculation loop to complete the estimated state quantity. Iterative calculation, on the right is the gain calculation loop to complete the Kalman gain calculation; the upper and lower dashed lines constitute two update processes, within the time update, complete the state one-step prediction One-step prediction P k/k-1 with the mean square error. After the time update is completed, if there is no measurement data at this time, the one-step prediction value will be output as the optimal estimation of the state.
  • the dual position alignment algorithm based on Kalman's optimal estimation adopts strapdown inertial navigation attitude update algorithm and speed update algorithm to update the angular and linear motion of the carrier in real time, and adopts the correction algorithm based on zero speed and the earth rotation angular rate for measurement Update and best estimate. Therefore, the optimal estimation accuracy has nothing to do with the accuracy of the indexing, and there is no need to know the exact position of the indexing mechanism. This is very beneficial in engineering practice. It avoids the design of complex stop structures and avoids the use of high-temperature-resistant measuring devices. Angle agency. This is the feature and advantage of the Kalman algorithm + dual position alignment method of the present invention.
  • GMD two-position precision alignment adopts the sequential processing flow as shown in Figure 8.
  • the effective interpretation of Z k in Figure 8 is to determine the validity of the measured data (formulas (4.4) and (4.8)), that is, to set the criterion of sensitive speed or sensitive angular rate to determine whether the drill collar is in The static state or whether it is guaranteed that the slight disturbance does not affect the accuracy of the alignment.
  • the state variable completes the time update, when the GMD probe is in a static or slightly disturbed state, the accelerometer and gyroscope data collected for a period of time are used to automatically determine whether the observation is valid, and the speed is completed according to sequential processing.
  • the measurement Z v update and the angular rate measurement Z ⁇ update calculate the Kalman gain, and realize the optimal estimation of the constant drift error of the X and Y horizontal gyroscopes and the constant drift error estimation of the Z-axis gyroscope (the constant drift error of the gyroscope)
  • the best estimate of is reflected in the drift error of the gyroscope and accelerometer contained in the state matrix X with ), and finally complete the optimal estimation of the attitude and azimuth misalignment angle.
  • Equation (5.6) The final result of the optimal estimation under the effective measurement equation is formula (5.6); formula (5.7) is the evaluation of the estimation effect after estimation. Equations (5.3) to (5.7) are the estimation process, which is a recursive process.
  • the basic flow of the Kalman dual position alignment algorithm is as follows:
  • the defined horizontal attitude angle namely the pitch angle and roll angle, corresponding to the drilling measurement, corresponding to the well inclination angle and the tool face angle
  • the defined azimuth angle is the azimuth angle of the northeast sky, Corresponding to the drilling survey term, it is the azimuth angle or the included angle with the geographic north;
  • the entire alignment process can be completed in about 300s, and the process is shown in Figure 9.
  • Step 1 Update attitude and speed
  • attitude update and speed update are existing technologies.
  • attitude update and speed update are existing technologies.
  • attitude update and speed update are existing technologies.
  • attitude update and speed update are existing technologies.
  • Quaternion is a mathematical method. In the strapdown inertial navigation algorithm, it is used as a convenient tool to describe the transformation relationship of the coordinate system and solve the attitude matrix.
  • the Euler's one-time rotation theorem shows that the limited rotation of a rigid body from one position to another can be realized by a rotation of a certain angle around a certain axis passing through the fixed point, and this rotation can be achieved by the following unit four Yuan number representation:
  • the angle ⁇ in the quaternion q represents the angle of one rotation
  • the vector ⁇ represents the direction of the axis of one rotation
  • the direction of ⁇ is used as the positive direction of the rotation angle ⁇ according to the right-hand rule.
  • the carrier’s angular velocity vector in real time and then the quaternion can be obtained.
  • the carrier’s attitude and azimuth information can be obtained, ⁇ , ⁇ ,
  • the initial quaternion can be obtained as:
  • the quaternion of the carrier can be continuously obtained and updated, so as to obtain the attitude conversion matrix of the carrier, so as to calculate the attitude information of the carrier in real time, ⁇ , ⁇ ,
  • the carrier here is the drill collar component that needs to be measured by GMD.
  • the velocity differential equation is the specific force equation, which is the basic relational formula for the inertial navigation solution.
  • g n [0 0 -g] T , which is the projection of gravitational acceleration in the navigation coordinate system.
  • f b refers to the three-component value of the carrier coordinate system b measured by the accelerometer in real time.
  • Each parameter in formula (5.8) is vector or vector.
  • ⁇ ie is the angular rate of the earth's rotation.
  • the radius of curvature of the meridian circle R M and the radius of curvature of the unitary circle R N can be calculated as follows:
  • Step 2 Perform Kalman filtering; the specific algorithm is divided into two parts: time update and measurement update;
  • Attitude update Substitute the updated quaternion in the 1.1 attitude update algorithm into the attitude transition matrix , Used to update the F matrix and W matrix in the Kalman state equation (4.2), so as to achieve Kalman's posture update.
  • the b system is fixedly connected to the IMU (Inertial Measurement Unit) and rotates with the carrier.
  • the origin is located at the sensitive center of the IMU position, which is represented by ox b y b z b, and is represented by an attitude matrix Represents the angular position relationship between the b system and the n system.
  • the attitude transition matrix between the navigation coordinate system and the carrier coordinate system is:
  • ⁇ k/k-1 is the discretization of the one-step transition matrix F of the 12 ⁇ 1 dimensional state, and ⁇ k/k-1 is the system noise allocation matrix;
  • Time update is just to calculate the update of the 12 state variables of the state variables under the real-time data collected by different gyroscopes and accelerometers, and the measurement data at this time is not used.
  • the measurement update is the measurement data to correct The error of the state update, realizes the optimal estimation (azimuth and horizontal attitude, drift of gyroscope and accelerometer, namely 9 of 12 variables).
  • the validity of the measured data value can be judged by judging whether the drill collar is in a static state or whether the external disturbance reaches a degree that does not affect the alignment accuracy. Only when the measurement data value is valid, the measurement update is performed, otherwise the measurement update is not performed, only the time update is performed, that is: the update result of the one-step prediction equation or the one-step prediction mean square error equation of the state in the time update is used as the output of the Kalman filter (That is, the horizontal posture information and azimuth information at this time are output from the formula (5.3)/(5.4)).
  • the setting for judging whether the drill collar is in a static state can be specifically: set the observed sensitive velocity observation (such as acceleration value) or sensitive angular rate observation (such as the root mean square value of the gyroscope angular rate), the value of which is less than a certain one
  • the measurement update is performed; if it is not satisfied, the measurement update is not performed, only the time update is performed.
  • the criterion of external disturbance can be whether the external mud disturbance or the measured value of the vibration sensor is less than the set threshold. If it is less, the alignment accuracy will not be affected and the measurement update will be performed. Otherwise, the measurement update will not be performed, only the time renew.
  • the measurement equations (4.4) and (4.8) are the velocity measurement based on the zero-speed constraint and the angular rate measurement based on the angular rate constraint of the earth's rotation, respectively.
  • the state estimation equation (5.6) is the Kalman filter value obtained from the final optimal estimation, including the initial alignment of the strapdown inertial navigation mathematics platform misalignment angle ⁇ n and gyro constant drift
  • accelerometer constant zero offset Equation (5.7) is the evaluation of the estimation effect after estimation.
  • the parameters of the high temperature inertial instrument are shown in Table 1.
  • the simulation process is the same as the analytical dual position alignment method.
  • the inclination angle is in the range of 0 to 90°, every 5 °Choose a position for simulation, a total of 19 positions, 40 Monte-Carlo simulations for each position and take the root mean square value.
  • the simulated well trajectories are divided into north-south and east-west directions, and the azimuths under different well inclination angles are analyzed. Alignment error, and the ability of inertial instrument to measure drift.
  • Simulation 1 The well trajectory is north-south, the vertical well attitude [0°,0°,0°] in the geographic coordinate system, and the horizontal well attitude is [90°,0°,0°],
  • Figure 10 shows the misalignment angle Error curve
  • Figure 11 is the constant drift estimation error of gyroscope and accelerometer respectively.
  • Simulation 2 The well trajectory is east-west, the vertical well attitude is [0°,0°,90°] in the geographic coordinate system, and the horizontal well attitude is [90°,0°,90°]. The following are from the vertical well The alignment accuracy and drift measurement capability under different well inclination angles, small well inclination angles and large well inclination angles are simulated. Finally, the simulation conclusions of the alignment accuracy and drift measurement capability under different well inclination angles and different directions are obtained.
  • Figure 12 is a simulation of the misalignment angle curve
  • Figure 13 is the constant drift estimation error curve of the accelerometer (b) and gyroscope (a). After the 180° indexing is completed, the constant drift error of the inertial instrument is quickly eliminated. This also eliminates the alignment error between the horizontal attitude and the azimuth. The final simulation result shows that the final azimuth misalignment angle estimation error is -0.1°, and the misalignment angle is only related to the random drift error of the inertial instrument.
  • Figure 4 shows that when the inclination angle is greater than 10°, the azimuth alignment accuracy error exceeds the design index of 1°.
  • the small well inclination angle is set to 15°, that is, the initial attitude angle is [15°,0°,90°]
  • the large well inclination angle is 70°, that is, the initial attitude angle is [70°,0°,90°]
  • the 20 Monte-Carlo simulation results are shown in Figure 14(a) and 14(b).
  • the attitude and azimuth misalignment error can quickly converge after 180° inversion, regardless of the small well inclination angle and the large well inclination angle, and the azimuth misalignment at the end of the alignment under the small well inclination angle of 15°
  • the mean angle is -0.0072°, and the standard deviation of 3 ⁇ is 0.4°; at a large inclination angle of 70°, the mean end azimuth misalignment angle of alignment is 0.1°, and the standard deviation of 3 ⁇ is 0.9°, both satisfying the 1° Bearing accuracy requirements.
  • Figure 15(a) and (b) show a simulation result of the drift estimation of the inertial instrument at a large inclination angle of 70°.
  • the constant drift estimation error of the gyroscope (corresponding to figure a) is [ 0.01,-0.02,-0.05]deg/h
  • the constant drift estimation error of the accelerometer (corresponding to Figure b) is [4.6,-0.5,-0.05]ug.
  • the Kalman optimal estimation can still accurately estimate the constant drift of the inertial instrument. Therefore, the algorithm designed in this paper can still achieve the azimuth error of 70° large well inclination angle of less than 1° when the current high temperature gyroscope has a large repeatability error of 2°/h.
  • Figure 16 shows that using the two-position Kalman + velocity measurement based on zero velocity and the optimal estimation of the angular rate measurement based on the angular rate constraint of the earth's rotation angle proposed in this paper, in the east-west trending well trajectory condition, when the well is deviated When the angle is less than 70°, the azimuth alignment accuracy can be maintained better than 1°. In a fully horizontal well section, the azimuth measurement accuracy better than 5° can still be achieved, and the result is much better than the dual position analytical method shown in Figure 4. The accuracy of the alignment.
  • the drift error of the Z-axis gyroscope can be guaranteed to be better than 0.2deg/h from the vertical well section (0°) to the east-west deflection angle (75°) section.
  • the method of the present invention can be used to estimate X/h from the vertical well section to the horizontal well section very well.
  • the drift error of the Y gyroscope can meet the estimation accuracy of the drift error of the Z-axis gyroscope at a large inclination angle in the east-west horizontal well direction.
  • the alignment method of multi-position+rotation position strapdown solution+Kalman+zero-speed correction speed measurement and angular rate measurement restricted by the earth’s rotation angular rate is especially suitable for strapdown using Coriolis vibration gyroscope.
  • Inertial navigation system The accuracy of the Coriolis vibratory gyroscope mainly depends on the processing accuracy, homogeneity uniformity of the resonator and the accuracy of the control circuit. However, due to the actual influence of the processing technology, the processing accuracy and material uniformity of the resonator cannot reach the perfect degree. This will inevitably cause errors in the angular rate estimation of the resonant gyroscope, and cause the azimuth alignment error of the strapdown inertial navigation system.
  • the method of the present invention is aimed at the drift error of the gyroscope, especially the Coriolis vibratory gyroscope, and simultaneously adopts the speed measurement of zero speed correction and the angular rate measurement of the earth rotation angular rate constraint to carry out the measurement update, and combines the indexing process.
  • the strap-down calculation algorithm can achieve the optimal estimation of the gyroscope drift error, thereby improving the accuracy of the GMD system's azimuth measurement.
  • the method of the present invention is applied to an inertial navigation system.
  • the inertial navigation system includes a three-axis gyroscope, a three-axis accelerometer, a shock absorber, and the gyroscope and the shock absorber are fixedly connected; the three-axis gyroscopes are set at 90 degrees or other angles to each other.
  • the inertial navigation system is a strapdown inertial navigation system.
  • the measurement method is applied to the north-seeking process of the Coriolis vibratory gyroscope to realize the initial alignment of the gyroscope.
  • Coriolis vibratory gyroscope is used in MWD system.
  • the attitude measurement method of the present invention can also be applied to a multi-point gyro compass measurement-while-drilling system or a multi-point gyro compass cable measurement system or a continuous navigation measurement system with zero-speed correction capability to realize the attitude measurement of an underground well.

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Abstract

一种用于定向钻进随钻测量技术的姿态测量方法，该方法采用在多个位置分别进行精对准的方法进行初始对准；方法步骤包括：S1、以陀螺仪的当前姿态和速度数据作为第一初值，在第一位置进行精对准；S2、捷联惯导系统转位至第n位置，转位过程中根据上一次精对准结果进行姿态和速度更新；S3、以姿态更新和速度更新的结果为第n初值，在第n位置进行第n次精对准，完成捷联惯导系统的初始对准，从而实现姿态测量。该方法适用于水平井的全井斜段的水平姿态与方位测量，特别是定向钻进陀螺随钻测量在大井斜井、水平井姿态测量应用，能够提升惯性仪表误差的可观测性，抑制陀螺仪的重复性误差，提高姿态测量精度。

Description

一种姿态测量方法 【技术领域】
本发明涉及定向钻进姿态测量技术领域，尤其是大井斜井、水平井的姿态测量方法以及定向钻进陀螺随钻测量方法。
【背景技术】
当前随着世界勘探领域逐步向复杂地区和特殊环境延伸，开发难度和开发成本将大大增加，勘探开发形势推动着井型的演变与发展，大位移井、超薄油层水平井、多分支井等复杂结构井在油气田勘探开发中所占的比例越来越大。随着旋转导向技术为代表的导向钻井技术的发展，尤其是在深层与超深层导向钻井应用中，对井眼轨迹控制精度的要求不断提高。
石油勘探开发对于高端陀螺仪的需求：能够满足高温、强振动且具备小体积和高精度的陀螺仪，一直是石油行业对于惯性技术矢志不渝的追求，尤其是针对定向钻井过程中，磁通门存在干扰的情况下，当前并非不需要陀螺仪，而是尚无适合的陀螺仪产品，能够在高温、强振动等恶劣环境下长时间正常工作。作为导向钻井应用的陀螺仪相关技术，恶劣环境下的可靠性是选择的重要依据，因此需要开发一种能够满足石油钻井测量领域中最为苛刻的使用场景，高温、强振动环境下的环境适应性问题、零偏重复性问题等。
现有的校准方法只是从外部环境干扰的抑制能力、计算量等方面存在的差异性出发，并没有考虑GMD特定的使用环境，即高温和强振动等恶劣环境，对惯性仪表造成的较大的漂移误差。但是惯性仪表这一实际存在的漂移误差会对现有校准方法的校准精度产生影响，在高温、强振动恶劣环境的工况下，零偏重复性误差是制约陀螺仪精度的主要瓶颈。
因此，有必要研究一种姿态测量方法来应对现有技术的不足，以解决或减轻上述一个或多个问题，提高井眼轨迹的施工精度。
【发明内容】
有鉴于此，本发明提供了一种姿态测量方法，具有容错能力和微小晃动下对准的能力，能够在不改变惯性仪表本身精度基础上，提升惯性仪表误差的可观测性，抑制陀螺仪逐次启动的重复性误差，从而提高姿态测量的精度。
一方面，本发明提供一种姿态测量方法，所述方法用于捷联惯导系统，其特征在于，采用在多个位置分别进行精对准的方法对陀螺仪重复性漂移进行抑制；
所述方法的步骤包括：
S1、以陀螺仪的当前姿态数据和速度数据作为第一初值，在第一位置进行第一次精对准；
S2、捷联惯导系统转位至第n位置，在转位过程中根据第n-1次精对准的结果进行姿态更新和速度更新；
S3、以姿态更新和速度更新的结果为第n初值，在第n位置进行第n次精对准，完成捷联惯导系统的初始对准；
其中，n从2开始做加1递增，重复步骤S2和S3，直至n＝k；k为所述方法所选用的位置的个数，且k大于等于2。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，所述多个位置具体为双位置，即k＝2。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，精对准采用卡尔曼算法实现。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，采用卡尔曼算法进行精对准的内容包括：时间更新和/或量测更新；
时间更新，根据系统采集的实时数据完成状态变量的更新，包含姿态更新和速度更新；
量测更新，用量测数据修正状态更新的误差，实现最优估计；
卡尔曼滤波采用零速修正的速度量测和地球自转角速率约束的角速率量测 进行量测更新和最优估计，以提高对准精度。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，所述方法用于钻井测量时，所述精对准初值的数据包括：井斜角、工具面角和方位角。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，量测更新的步骤包括：
1)判断量测数据值是否有效，若有效，进入步骤2)，否则，不进行更新，将时间更新结果作为卡尔曼滤波的最终结果；
2)根据量测数据值对状态更新结果进行修正，并根据修正结果和时间更新结果，计算增益系数，得到最优状态估计。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，判断量测数据值是否有效通过判断钻铤是否处于静止状态和/或判断外部扰动是否满足对准要求来实现；若钻铤处于静止状态和/或外部扰动满足对准要求，则判定量测数据值有效，否则判定量测数据值无效。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，判断钻铤是否处于静止状态具体为：判断敏感速度观测量和/或敏感角速率观测量是否小于判定阈值，若是，则判定钻铤处于静止状态，否则不处于静止状态。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，判断外部扰动是否满足对准要求具体为：判断外部泥浆的扰动量或振动传感器感应到的振动量是否小于设定的阈值；若是，则判定外部扰动量满足对准要求，否则不满足；
上述几个判断条件中的阈值的具体数值根据钻井地质环境、所处深度等实际情况而定。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，敏感速度观测量为陀螺仪的实时加速度值；敏感角速率观测量为陀螺仪角速率均方根值。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，步骤2) 的具体内容包括：按照序贯处理方法，分别求解由零速修正的速度量测Z v与地球自转角速率约束的角速率量测Z ω组成的量测方程，实现X、Y水平陀螺仪常值漂移误差最优估计与Z轴陀螺仪常值漂移误差估计，最终完成姿态与方位失准角的最优估计。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，在时间更新时，完成状态一步预测与均方误差一步预测。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，转位过程中的姿态更新采用四元数法进行更新。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，所述测量方法还包括在第一位置的粗对准，并以粗对准的结果作为第一初值进行第一次精对准。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，卡尔曼状态方程具体为：
Figure PCTCN2020090520-appb-000001
其中，
Figure PCTCN2020090520-appb-000002
Figure PCTCN2020090520-appb-000003
分别为加速度计和陀螺仪在载体坐标系的随机白噪声；
Figure PCTCN2020090520-appb-000004
为导航坐标系与载体坐标系的姿态转移矩阵；X和
Figure PCTCN2020090520-appb-000005
代表卡尔曼滤波状态变量；
Figure PCTCN2020090520-appb-000006
Figure PCTCN2020090520-appb-000007
δv n为速度误差、φ n为捷联惯导数学平台失准角、
Figure PCTCN2020090520-appb-000008
为陀螺常值漂移，
Figure PCTCN2020090520-appb-000009
为加速度计常值零偏；ω ie为地球的自转角速率；L为纬度；T表示矩阵的转置；
f n＝[0 0 g]，g为重力加速度；
导航坐标系与载体坐标系的姿态转移矩阵
Figure PCTCN2020090520-appb-000010
具体为：
Figure PCTCN2020090520-appb-000011
式中，θ表示俯仰角，ψ表示航向角，γ表示横滚角。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，进行时间更新的公式包括：
状态一步预测方程：
Figure PCTCN2020090520-appb-000012
以及一步预测均方误差方程：
Figure PCTCN2020090520-appb-000013
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，进行速度量测更新时采用的公式为：
速度量测方程：Z v＝δv n＝H vX+V v，其中，H v＝[I 3×3 0 3×3 0 3×3 0 3×3]；
进行地球自转角速率量测更新时采用的公式为：
地球自转角速率量测方程：
Figure PCTCN2020090520-appb-000014
式中，
V v为导航坐标系中的速度量测噪声；
V ω是指角速率量测噪声；
v n为输出速度，δv n为速度误差，将δv n作为量测数据，I表示单位矩阵，Z ω表示角速率观测量，Z ν表示速度观测量。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，计算卡尔曼滤波增益的公式为：
卡尔曼滤波增益方程(5.5)：
Figure PCTCN2020090520-appb-000015
完成姿态最优估计的公式为：
状态估值方程(5.6)：
Figure PCTCN2020090520-appb-000016
状态估计均方误差方程(5.7)：P k/k＝(I-K kH k)P k/k-1。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，采用欧拉解析法进行静基座粗对准，根据加速度计与陀螺仪的数据直接进行计 算。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，粗对准的公式包括：
俯仰角
Figure PCTCN2020090520-appb-000017
横滚角
Figure PCTCN2020090520-appb-000018
航向角
Figure PCTCN2020090520-appb-000019
其中，
Figure PCTCN2020090520-appb-000020
分别为载体上三分量加速度的量测数据，
Figure PCTCN2020090520-appb-000021
分别为载体上三分量陀螺仪的量测数据；所述陀螺仪的量测数据主要指角速率。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，第一次卡尔曼对准和第二次卡尔曼对准使用的时间均为130s以内，能够实现的水平井下方位对准精度为1deg以内。
另一方面，本发明提供一种随钻测量系统，所述系统包括捷联惯导系统，所述捷联惯导系统包括三轴陀螺仪、三轴加速度计；其特征在于，采用如上任一所述的姿态测量方法，抑制陀螺仪的重复性漂移误差，提高定向钻进的随钻测量的精度。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，所述陀螺仪为哥氏振动陀螺仪。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，所述陀螺仪为高温谐振式陀螺仪；
所述捷联惯导系统还包括减振器，所述减振器与所述高温谐振式陀螺仪固联。
如上所述的方面和任一可能的实现方式，进一步提供一种实现方式，所述高温谐振式陀螺仪包括谐振子、电路板、压电陶瓷、支撑基座、外壳，接线柱，所述谐振子置于外壳内并与支撑基座连接，压电陶瓷通过导电金属丝与接线柱相连，所述电路板实现信号的传输，在所述陀螺仪内部元件的关键 工艺点上进行固联；固联的关键工艺点位于压电陶瓷与谐振子之间、接线柱与压电陶瓷之间、接线柱与电路板之间、支撑基座与谐振子之间、外壳与支撑基座之间。
再一方面，本发明提供一种连续导航测量系统，所述系统包括捷联惯导系统，所述捷联惯导系统包括三轴陀螺仪、三轴加速度计；其特征在于，采用如上任一所述的姿态测量方法，抑制陀螺仪的重复性漂移误差，提高导航过程中的姿态测量精度。
姿态测量信息，包含水平姿态角和方位角，是三个参量：通常，将俯仰角(井斜角)和横滚角(工具面角)称之为水平姿态，航向角(对准方位)称之为方位角。初始对准的目的就是通过实时采集加速度计与陀螺仪的数据，进行相关的算法处理，从而获取载体的姿态信息(水平姿态角和方位角)。
与现有技术相比，本发明可以获得包括以下技术效果：本发明的对准方法在泥浆晃动引起的干扰角速率大于地球自转角速率时依然可正常寻北，具有较好的容错能力和微小晃动下对准的能力，能够在不改变惯性仪表本身精度基础上，提升惯性仪表误差的可观测性，实现惯性仪表误差的最优估计，从而提高初始对准精度；基于卡尔曼最优估计的双位置对准算法采用了捷联惯导姿态更新算法与速度更新算法去实时更新载体的角运动与线运动，采用基于零速和/或地球自转角速率修正算法进行量测更新和最优估计,使得最优估计精度与转位的精度无关，也无需知道转位机构的准确位置，这在工程实际中是非常有益的，避免了复杂止档结构的设计，也避免了使用耐高温的测角机构；转位置消除漂移误差或者测漂，实际只能实现水平陀螺仪(即x与y陀螺仪)的测漂，不能实现大井斜角下的Z轴陀螺仪的测漂，通过零速修正和恒定角速率修正，提供约束关系，则尤其实现Z轴陀螺仪的测漂。
当然，实施本发明的任一产品并不一定需要同时达到以上所述的所有技术效果。
【附图说明】
为了更清楚地说明本发明实施例的技术方案，下面将对实施例中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其它的附图。
图1是本发明一个实施例提供的单轴陀螺仪转位置消除零偏原理图；
图2是本发明一个实施例提供的双位置对准(即转位对准)时南北走向井轨迹对准失准角曲线图；
图3(a)是本发明一个实施例提供的转位法纠偏时南北走向井轨迹的陀螺仪常值漂移估计误差曲线图；
图3(b)是本发明一个实施例提供的转位法纠偏时南北走向井轨迹的加速度计常值漂移估计误差曲线图；
图4是本发明一个实施例提供的转位法纠偏时井轨迹东西走向时水平姿态与方位对准失准角曲线图；
图5(a)是本发明一个实施例提供的转位法纠偏时东西走向井轨迹的陀螺仪常值漂移估计误差曲线图；
图5(b)是本发明一个实施例提供的转位法纠偏时东西走向井轨迹的加速度计常值漂移估计误差曲线图；
图6是本发明一个实施例提供的双位置纠偏方法不同常值漂移误差下得到的全井斜方位对准精度曲线图；
图7是本发明一个实施例提供的双位置卡尔曼滤波算法的流程图；
图8是本发明一个实施例提供的双位置卡尔曼算法序贯处理方法流程图；
图9是本发明一个实施例提供的双位置+卡尔曼对准流程示意图；
图10是本发明一个实施例提供的双位置+卡尔曼对准法纠偏时南北走向井轨迹失准角误差曲线图；
图11(a)是本发明一个实施例提供的双位置+卡尔曼对准法纠偏时南北走向井轨迹陀螺仪漂移估计误差图；
图11(b)是本发明一个实施例提供的双位置+卡尔曼对准法纠偏时南北走向井轨迹陀螺仪漂移估计误差图；
图12是本发明一个实施例提供的双位置+卡尔曼对准法纠偏时竖直井失准角误差曲线图；
图13(a)是本发明一个实施例提供的双位置+卡尔曼对准法纠偏时竖直井陀螺仪漂移估计误差曲线图；
图13(b)是本发明一个实施例提供的双位置+卡尔曼对准法纠偏时竖直井加速度计漂移估计误差曲线图；
图14(a)是本发明一个实施例提供的双位置+卡尔曼对准法纠偏时东西向井轨迹小井斜失准角估计误差曲线图；
图14(b)是本发明一个实施例提供的双位置+卡尔曼对准法纠偏时东西向井轨迹大井斜失准角估计误差曲线图；
图15(a)是本发明一个实施例提供的双位置+卡尔曼对准法纠偏时东西向井轨迹70°大井斜角下陀螺仪的常值漂移估计误差图；
图15(b)是本发明一个实施例提供的双位置+卡尔曼对准法纠偏时东西向井轨迹70°大井斜角下加速度计的常值漂移估计误差图；
图16是本发明一个实施例提供的双位置+卡尔曼对准法纠偏时东西向井轨迹全井斜角下GMD对准失准角误差仿真曲线图；
图17(a)是本发明一个实施例提供的双位置+卡尔曼对准法纠偏时东西向井轨迹全井斜角下陀螺仪常值漂移估计误差曲线图；
图17(b)是本发明一个实施例提供的双位置+卡尔曼对准法纠偏时东西向井轨迹全井斜角下加速度计常值漂移估计误差曲线图；
图18是标准捷联惯导系统的姿态测量原理图；
图19是本发明提供的导向钻井：水平井示意图。
【具体实施方式】
为了更好的理解本发明的技术方案，下面结合附图对本发明实施例进行详细描述。
应当明确，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有作出创造性劳动前提下所获得的所有其它实施例，都属于本发明保护的范围。
在本发明实施例中使用的术语是仅仅出于描述特定实施例的目的，而非旨在限制本发明。在本发明实施例和所附权利要求书中所使用的单数形式的“一种”、“所述”和“该”也旨在包括多数形式，除非上下文清楚地表示其他含义。
针对现有技术的不足，本发明姿态测量方法，采用卡尔曼+多位置(尤其双位置)+零速的方法进行大井斜角的校准，并对恒定角速度进行修正。如图19所示，水平井包含了：竖直(井)段、靶前位移(斜井段)、水平(井)段，其中定义竖直段的井斜角为0°，靶前位移(斜井段)是指井斜角大于0°到90°这个区段，通常又分为小井斜角(如0°～20°)和大井斜角(如大于70°)，没有明确的定义，一般是业内俗称，水平段是指井斜角为90°这一段。定义全井斜，是指涵盖了从竖直段到水平段，井斜角从0°到90°。双位置是其中的一种实现方案，实际任何位置都可以。从机械结构设计的角度来说，双位置对准，方便机械结构设计，即通过机械止档的设计，实现准确的两点定位。
本发明测量方法推理逻辑如下：
1：陀螺仪导向的基本原理
陀螺导向是基于陀螺罗盘原理(Gyrocompass)原理,主要是使用惯性器件(加速度计与陀螺仪)去测量地球自转角速率矢量与重力加速度矢量，从而计算出载体与地理北向的夹角。
地球的自转角速率ω ie为固定值15.041067°/h(约0.0042°/s)，被测载体所处位置的经度与纬度分别为λ和L，采用“东北天”地理坐标系。
根据陀螺导向的原理，地球自转角速率的水平分量为ω N，其大小取决于测量地点的纬度L。
ω N＝ω iecosL             (1.1)
如在北京纬度是40°，地球自转的水平分量约为11.52°/h，纬度越高水平分量越小，接近极点位置水平分量趋于零。
假设陀螺仪的敏感轴与载体运动方向同相，定义方位角ψ为陀螺仪敏感轴与北向夹角，则得到陀螺仪的输出值为：
ω ob＝ω Ncosψ+B＝ω iecosLcosψ+B         (1.2)
式(1.2)中，ω ob为陀螺仪的输出值，即观测值，B为陀螺仪的零偏。
求解式(1.2)，就可以计算得到载体的方位角ψ，此外，由式(1.2)可知，陀螺仪的测量数据包含了陀螺仪本身的零偏B，其值的大小会直接影响方位角计算结果，通常通过多点转位或者连续旋转调制等方式消除，图1给出了单轴陀螺仪通过转位机构旋转改变其敏感方向工作原理示意，为了方便转位机构机械设计，采用简单的0°、180°两位置转位方法，陀螺仪的输出分别为：
ω ob(0)＝U 1/SF 1＝ω ieocsLcosψ+B 1        (1.3)
ω ob(180)＝U 2/SF 2＝-ω iecosLcosψ+B 2          (1.4)
式(1.3)、(1.4)中，SF 1、SF 2，U 1、U 2，B 1、B 2分别是指在0°和180°位置下陀螺仪的标度因子、输出(模拟量或者数字量)和零偏。
设定GMD寻北的精度为1°，忽略陀螺仪的标度因子误差，由(1.3)、(1.4)可得到单轴陀螺仪的方位测量估计为：
Figure PCTCN2020090520-appb-000022
式(1.5)中，ε B是转位补偿后的残余漂移误差，对上式取泰勒展开并忽略高阶项，得到两位置下的估计误差(精度)为
Figure PCTCN2020090520-appb-000023
从式(1.6)可知，采用单陀螺两位置转位时，转位的两个位置选择在东 西向附近(ψ 1＝90°、270°)估计误差最小，此时的估计误差为：
Figure PCTCN2020090520-appb-000024
式(1.7)给出了陀螺仪寻北估计精度误差的基本公式，可以看出，两位置转位的寻北精度与陀螺仪的残余漂移误差、当地的纬度相关。
2：导向原理(初始对准方法)
导向原理采用欧拉角解析法，欧拉角解析法利用陀螺和加速度计信息直接求取载体的俯仰角(井斜角)θ，横滚角(工具面)γ和航向角(方位角)Ψ，在给出本发明解析双位置对准以及双位置卡尔曼最优估计对准方案之前，首先利用欧拉角分析方法，给出粗对准的原理与精度极限。
由于钻井施工地点地理位置已知，此时就能准确获取地球自转角速度矢量在地理坐标系的分量和重力矢量，如下式：
Figure PCTCN2020090520-appb-000025
其中，g、ω ie、L分别表示当地重力加速度大小、地球自转角速率大小和当地纬度，记地球自转角速度的北向分量ω N＝ω iecosL和天向分量ω U＝ω iesinL。
在静基座粗对准过程中，GMD系统中陀螺和加速度计测量到的分别是重力矢量和地球自转角速度在载体系下的投影，忽略泥浆晃动干扰的影响，载体上三分量陀螺仪与三分量加速度的量测数据为：
Figure PCTCN2020090520-appb-000026
Figure PCTCN2020090520-appb-000027
其中，
Figure PCTCN2020090520-appb-000028
粗对准时间一般都很短，惯性仪表的量测数据值一般取一段时间内的平滑均值，在惯性仪表无明显的趋势项漂移误差时，平滑时间越长，越能获得比较好的精度，在综合考虑粗对准时间与对准精度的情况下，平滑的时间长 短可以通过对Allan方差测试数据进行判断分析，平滑的最优时间选取依据是Allan方差“触底”的时间。
由式(2.3)，可求得俯仰角
Figure PCTCN2020090520-appb-000029
求得横滚角
Figure PCTCN2020090520-appb-000030
在获得
Figure PCTCN2020090520-appb-000031
和
Figure PCTCN2020090520-appb-000032
的基础上，代入式(2.2)可得
Figure PCTCN2020090520-appb-000033
求解方位角为
Figure PCTCN2020090520-appb-000034
式(2.4)、(2.5)、(2.7)即构成了欧拉角粗对准的基本算法，下面分析欧拉解析方法静基座对准的极限精度。
考虑加速度计和陀螺仪的零偏误差：
Figure PCTCN2020090520-appb-000035
式(2.8)中，
Figure PCTCN2020090520-appb-000036
分别表示载体系与导航系下的加速度计的零偏误差，ε b、ε n分别表载体系与导航系下的陀螺仪的零偏误差。
求解一个方向微分时并令另外两个方向角度为零，分别对(2.4)、(2.5)、(2.7)两边进行微分并忽略二阶小量得，
Figure PCTCN2020090520-appb-000037
Figure PCTCN2020090520-appb-000038
Figure PCTCN2020090520-appb-000039
式(2.9)、(2.10)和(2.11)确定了静基座对准的极限精度，即为粗对准的解析法的公式，通过加速度计与陀螺仪的数据直接进行计算即可。静基座条件下的姿态对准精度主要取决于东向与北向的加速度计漂移误差，而方位对准精度主要取决于东向陀螺的漂移误差以及东向加速度计的漂移误差。
卡尔曼最优估计中，上标的^号，代表估计值，或者计算值，不带的，就是表示状态值。如，井斜角θ的估计值是
Figure PCTCN2020090520-appb-000040
此外，式(2.4)、(2.5)、(2.7)中选取的加速度计与陀螺仪的量测数据值，可以有多种方式，通常会选取一段时间采样值的均值，取样时间和极限精度，通常通过Allan方差的方法进行表述，将Allan方差的最低点作为精度极限的评价，因此，积分时间越长其平滑后的精度越高，但是对于存在趋势项误差或者漂移误差的情况，积分时间的长度取决于漂移误差的时间常数。当存在采样过程中的异常数据，或者此时钻铤的意外扰动时，带来了测量误差，这也是粗对准的最大风险和问题。
3：转位置index消除常值零偏的方法与原理(即双位置消零偏方法)
传统消除漂移误差、提高方位对准精度的方法是采用转位置index。
假定惯性仪表的常值零偏在转位前后数值不变，并忽略转动前后位置的角运动和线运动干扰，通过绕一个方向转动IMU，从而构造两个位置下的姿态转移矩阵，增加常值零偏的可观测性。实际应用中，受限于惯性仪表的尺寸与GMD探管的细长杆尺寸特性，转位机构的设计只能是绕探管的轴向，也就是绕Z轴陀螺仪的输入轴方向。
陀螺仪转位前后位置是b 1和b 2，在对准时间内对应的陀螺仪的采样输出均值分别为
Figure PCTCN2020090520-appb-000041
记加速度计转位前后采样输出均值分别为
Figure PCTCN2020090520-appb-000042
和
Figure PCTCN2020090520-appb-000043
假设b 1与b 2位置夹角为β，由此构成的状态转移矩阵为
Figure PCTCN2020090520-appb-000044
Figure PCTCN2020090520-appb-000045
则b 1位置和b 2位置惯性仪表输出之间存在关系式：
Figure PCTCN2020090520-appb-000046
考虑到转位过程时间很短，忽略随机常值中的一阶马尔科夫过程，并认为转位前后惯性仪表的常值漂移不变，只考虑随机漂移的影响，此外，由于陀螺仪绕Z轴旋转，Z轴陀螺仪与加速度计转位前后敏感方向不变，无法实现Z轴常值漂移的分离，当只考虑水平轴惯性仪表的输出时，
Figure PCTCN2020090520-appb-000047
式(3.2)可得b 2位置的水平陀螺输出为：
Figure PCTCN2020090520-appb-000048
同样可得b 2位置的水平加速度计的输出为：
Figure PCTCN2020090520-appb-000049
式(3.3、(3.4)可以得出，理论上任何微小转角β都可以分离出水平惯性仪表的常值漂移，当转角β为180°时，
Figure PCTCN2020090520-appb-000050
最大，常值漂移误差的分离受随机漂移的影响最小，不考虑转位过程的随机漂移影响，此时求得水平陀螺常值漂移估计值为：
Figure PCTCN2020090520-appb-000051
水平加速度计零偏估计值为：
Figure PCTCN2020090520-appb-000052
求得双位置校准后加速度计的估计值为：
Figure PCTCN2020090520-appb-000053
双位置校准后陀螺仪的估计值为：
Figure PCTCN2020090520-appb-000054
而Z轴的加速度计与陀螺仪不可观测，直接取转位前后的均值作为校准后的估计值：
Figure PCTCN2020090520-appb-000055
根据校正后的陀螺仪与加速度计的估计值，采用类似于单位置欧拉角解析粗对准原理，可求得校准后的倾角为：
Figure PCTCN2020090520-appb-000056
校准后的工具面角为：
Figure PCTCN2020090520-appb-000057
校准后的方位角为：
Figure PCTCN2020090520-appb-000058
式(3.7)～(3.9)构成了绕Z轴转位180°解析双位置对准的基本算法。
解析双位置解决了惯性仪表常值漂移误差校准的问题，提高了对准精度尤其是方位对准精度，对于小倾角测量，对准的主要误差来源于转位机构的 误差与惯性仪表的随机漂移误差，由于采用0-180°转位设计，只关注最终的转位定位精度，方便了转位机构的设计，在实际应用中，可以通过止档结构设计提高转位定位精度，简化了设计；对于随机漂移误差，假设每个位置的对准时间都是t，测试得到的陀螺仪的随机游走系数为
Figure PCTCN2020090520-appb-000059
则得到t时间内的统计均方差为
Figure PCTCN2020090520-appb-000060
设置总对准时间为300s，假设每个位置的对准时间为145s，由此带来的陀螺仪随机误差约为ε w＝0.017deg/h，对于噪声为
Figure PCTCN2020090520-appb-000061
的石英挠性加速度计，在100Hz的频带下，随机误差均方值为20μg，根据欧拉解析法方位对准精度极限的分析公式(2.11)，设置纬度40°N，可以求得随机误差带来的方位误差约是0.1deg，在如下的仿真中，会得出类似的结论。
对于定向钻进测量应用，大井斜角以及不同的轨迹方向下，通过仿真分析双位置解析法能够测量的精度极限与误差机理，仿真过程如下：
陀螺仪与加速度计的误差参数如表1高温惯性仪表仿真参数设置，设置初始位置为[116°E,40°N,100m]，在前145s处于第一对准位置，在146～155s期间沿着探管Z轴方向转动180°至第二位置，然后继续对准145s，对准总时间300s，井斜角在0～90°范围，每1°取一位置，共91个位置，每个位置做40次Monte-Carlo仿真并取均方根值。
表1 高温惯性仪表仿真参数设置表
Figure PCTCN2020090520-appb-000062
仿真一：井轨迹为南北走向，地理坐标系下的竖直井姿态方位[0°,0°,0°]，水平井姿态方位为[90°,0°,0°]，图2为对准失准角误差曲线，图3(a)和图3(b)依次为陀螺仪与加速度计的常值漂移估计误差。
从图2可以看出，当被测井轨迹是南北走向时，方位对准精度不受井斜 角的影响，也就是从竖直井段到水平井段，方位测量误差始终保持在0.1°附近，这也是符合公式(2.11)的结论，从初始对准的机理也不难理解，方位失准角与等效东向陀螺的精度相关，由于在南北走向时，从竖直井段到水平井段，东向陀螺仪始终能够被转位调制，也就是东西陀螺仪的常值漂移始终可观测，也就是通过转位的方式在任何井斜角下均可以消除等效东向陀螺的常值漂移。最终方位对准精度主要是取决于东向陀螺仪的随机漂移，图2仿真结果可以验证此结论。此外，图2中的东向失准角与图3(b)中的Z轴加速度计的估计误差曲线，可以看出Z轴加速度计随着倾角的增大，可观测性变差，当Z轴向南北方向倾斜时，导致了东向失准角误差随着倾角的增大而增大，但是其误差远小于目标精度指标，该项影响可以忽略。
仿真二：井轨迹为东西走向。地理坐标系下，竖直井姿态方位坐标为[0°,0°,90°]，水平井姿态方位坐标为[90°,0°,90°]，仿真结果如图4所示。
由图4可知，当井轨迹是东向走向时，随着井斜角的增大，方位失准角的估计误差也明显增加，最为主要的原因是当井斜角增大，Z轴陀螺仪成为东向陀螺仪的误差的主要贡献者，而转位是绕Z轴旋转的，Z轴的常值漂移本身不可观测，从而直接造成了方位失准角的误差，从图4还可以看出，为了保证方位测量精度优于1°，则井斜角不能超过10°。
对于双位置解析式对准，可以通过降低陀螺仪的常值漂移来提高大倾角下的方位测量精度，图6给出了不同常值漂移下的陀螺仪在不同倾角下的方位测量精度仿真曲线，可以看出，井轨迹测量精度要求是1°时，为了保证在大井斜角下的精度，要求陀螺仪的常值漂移小于0.2deg/h，而对于高温、强振动恶劣环境下的工况，零偏重复性误差是制约陀螺仪精度的主要瓶颈，研制满足使用工况下的0.2deg/h常值漂移误差的陀螺仪是非常有挑战的。
对于解析式双位置对准，在惯性器件精度一定的前提下，通过转位校准的方式，可以有效地提升东西轨迹下小井斜角以及全井斜角(0°～90°)南北走向轨迹的方位精度，但对于大井斜角下的东西走线的方位精度仍然不能满足使用要求，因此丞待一种更为有效的方法，在惯性器件精度受限的情况 下，提升大井斜角的方位测量精度。
4：双位置+卡尔曼的对准方法
本发明采用多位置+卡尔曼的对准方法来解决大倾角下东向陀螺的测漂问题。
该方法的内容包括：
导航坐标系取为东北天地理坐标系，建立12维惯导系统精对准数学模型，卡尔曼滤波器的状态变量为：
Figure PCTCN2020090520-appb-000063
式(4.1)中分别为：速度误差δv n、捷联惯导数学平台失准角φ n、高温陀螺常值漂移
Figure PCTCN2020090520-appb-000064
和高温加速度计常值零偏
Figure PCTCN2020090520-appb-000065
与
Figure PCTCN2020090520-appb-000066
主要是由高温惯性仪表的逐次启动重复性误差带来的，根据静基座下捷联惯导系统的误差模型并忽略小量误差，可得状态方程为：
Figure PCTCN2020090520-appb-000067
上式中，
Figure PCTCN2020090520-appb-000068
式(4.3)中
Figure PCTCN2020090520-appb-000069
分别为加速度计和陀螺的在载体坐标系(b系)随机白噪声，经测试验证，在经过综合温度补偿并消除Warm-up因素后，惯性仪表的输出可以表征为零均值正态分布，实际应用中，通常用Allan(阿伦)方差求解各模型系数，作为惯性仪表模型估计的先验值。
Figure PCTCN2020090520-appb-000070
g是重力加速度，f n＝[0 0 g]，×定义为反对称矩阵算式，定义向量：H＝[a b c],定义其反对称矩阵为
Figure PCTCN2020090520-appb-000071
GMD系统(Gyro Measurement while Drilling System，陀螺仪随钻测 量系统)静基座对准时载体静止，导航解算的输出速度v n即为速度误差δv n，将δv n作为量测数据，则量测方程为：
Z v＝δv n＝H vX+V v        (4.4)
其中，V v为导航坐标系中的速度量测噪声，δv n为速度误差，I表示单位矩阵，X代表卡尔曼滤波状态变量；Z ν表示速度观测量，H v＝[I 3×3 0 3×3 0 3×3 0 3×3]。
单位置卡尔曼对准的可观测性理论分析相对成熟，采用静基座下卡尔曼最优估计对准方式，φ U、ε N、ε U可观测性弱，而
Figure PCTCN2020090520-appb-000072
和ε E完全不可观测。单位置静基座卡尔曼对准无法估计东向与北向的加速度计常值漂移以及东向陀螺仪的误差，而东向加速度计误差决定了北向失准角，北向加速度计误差决定了东向失准角，方位失准角主要取决于等效东向陀螺误差，因此，在静基座条件下，采用单位置Kalman最优估计初始对准的方法，由于核心惯性仪表的可观测性弱，初始对准的精度受制于惯性仪表的常值漂移，而水平姿态对准与方位对准的收敛时间分别取决于水平加速度计的随机漂移与东向陀螺仪的角度随机游走系数。
对于导向钻进测量应用，当前高温的石英挠性加速度计的精度基本能够满足静基座下姿态对准精度要求，陀螺仪的精度尤其是逐次启动的重复性误差成为制约方位对准精度的核心因素。方位测量的精度提高有多种途径，一方面，是惯性仪表本身精度的提升，从根本上去解决影响重复性误差的因素，如惯性仪表的敏感单元精密加工、静平衡与动平衡、材料特性优化、控制电路优化等，但是存在研发周期长、成本代价高等问题；另一方面，从校准的角度，利用当前惯性仪表的特性，通过外部校准或者内部校准，从而实现提高惯性系统精度的目的，而外部校准，通常采用多位置转位+卡尔曼算法的方式进行校准。
双位置对准方法从本质上是属于静基座欧拉角初始对准，解析双位置对准无法实现惯性仪表误差的最优估计，尤其是在东西方向井轨迹下，由图4 可知，当倾角大于10°时，方位对准精度急剧变差。此外，由于解析法只是通过拾取一段时间的载体上惯性仪表的输出信息作为观测量，其对准精度受限于载体在采样时间段内的静止无晃动的理想程度，由于GMD工作于停钻寻北状态时，泥浆马达可能还在工作，当泥浆晃动引起的干扰角速率大于地球自转角速率时，解析双位置对准无法正常工作。基于最优估计的卡尔曼多位置对准，具有信息的容错能力，具有微小晃动下对准的能力，并能够在不改变惯性仪表本身的精度基础上，提升了惯性仪表误差的可观测性，实现了惯性仪表误差的最优估计，从而提高初始对准精度。受限于探管的狭小尺寸，绕探管轴向的两位置转位是本发明的优选方案。
和静基座下卡尔曼最优估计初始对准建立的状态方程一样，双位置卡尔曼最优估计的状态方程如式(4.2)，假设转位时间很短，认为常值漂移误差
Figure PCTCN2020090520-appb-000073
Figure PCTCN2020090520-appb-000074
在转位前后是固定不变的，类似于双位置解析法对准，通过外部旋转去改变惯导系统的姿态矩阵
Figure PCTCN2020090520-appb-000075
从而增加系统状态变量尤其是惯性仪表常值漂移的可观测性，双位置方法实现精对准的同时，估计了惯性仪表的误差。同样，当转角180°时，姿态矩阵
Figure PCTCN2020090520-appb-000076
的变化量最大，被估计状态的可观测性最强，求解方程(4.5)与(4.6)，
静基座下的GMD的姿态误差方程如式(4.5)所示：
Figure PCTCN2020090520-appb-000077
静基座下GMD的速度误差方程如式(4.6)所示：
Figure PCTCN2020090520-appb-000078
通过转位180°可以实现
Figure PCTCN2020090520-appb-000079
和
Figure PCTCN2020090520-appb-000080
和
Figure PCTCN2020090520-appb-000081
的最优观测，前者可以提高φ E、φ N的估计精度，后者可以提高φ U的估计精度，而在小倾角下的
Figure PCTCN2020090520-appb-000082
本身可观测 度高，所以对于绕GMD探管轴向转位的方案，作为传统静基座对准卡尔曼最优估计方法，当只采用速度误差δv n作为观测方程时，Z轴陀螺漂移ε z的可观测性最差，由此限制了GMD大倾角工作时的方位测量精度。
根据图18的标准捷联惯导系统方位测量原理可知，当Z轴进行转位置时，根据公式(3.5)-(3.9)，X轴陀螺仪、Y轴陀螺仪，可以通过转位的方式分离重复性误差。而当井斜角很大时，尤其是东西走向时，Z轴陀螺仪将成为东向(西向)陀螺仪，而受限于GMD的尺寸，转位机构只能绕Z轴，因此，大倾角下，Z轴陀螺仪将无法通过转位置的方式分离误差系数。此时，如果只有零速度修正，无法实现Z轴陀螺仪的重复性漂移误差的估计。根据式(2.9)、(2.10)、(2.11)可知，方位对准精度主要取决于东向陀螺仪的漂移误差，而此时Z轴陀螺仪漂移误差无法估计，从而使得方位精度无法满足要求。
为了实现在大井斜角下Z轴陀螺仪常值漂移误差的估计，需要增加观测量，本文采用静基座下地球自转角速率作为新的观测量，在获取水平姿态的最优估计后，利用载体系在导航系下的投影与导航系下地球角速率的差值作为卡尔曼的观测信息。通过仿真可知，Z轴陀螺仪的漂移误差得到了很好的估计。
其测量方程如下：
Figure PCTCN2020090520-appb-000083
由此得到量测方程为：
Figure PCTCN2020090520-appb-000084
式(4.8)中，V ω是指角速率量测噪声，Z ω表示角速率观测量。
至此，建立了完整的卡尔曼最优估计状态方程(4.2)，量测方程如式(4.4)与式(4.8)。
本部分相关含义说明：
惯性仪表的误差模型，静基座下，忽略标度因子误差与安装误差，陀螺 在载体坐标系输出模型可以表示为：
Figure PCTCN2020090520-appb-000085
其中
Figure PCTCN2020090520-appb-000086
陀螺仪采样输出的均值，ω b为陀螺仪的真实角速率输入值，ε 0为陀螺仪的常值漂移，ε r为慢变漂移，ε w为快变漂移。
根据Allan方差概念，ε 0主要是逐次启动的重复性误差，可以用随机常数表示，其误差模型为：
Figure PCTCN2020090520-appb-000087
慢变漂移ε r代表陀螺仪的趋势项，表征Allan方差中的速率斜坡项，通常可以用一阶马尔科夫过程描述，即：
Figure PCTCN2020090520-appb-000088
式(4.11)中，τ g为马尔科夫过程的相关时间，w r是白噪声。
根据高温陀螺仪样机的Allan方差可得，通过综合误差补偿，抑制了陀螺仪和时间相关的趋势项误差，实现了陀螺仪Allan方差“触底”时间后可以保持较长的时间，因此，实际上马尔科夫相关时间较长，在对准时间内可以忽略不计，陀螺仪的输出模型可简化为：
Figure PCTCN2020090520-appb-000089
其中，陀螺仪的零偏误差为：
ε＝ε 0+ε w           (4.13)
通常用角度随机游走系数ARW表示和白噪声相关的项ε w。
同样，加速度计输出模型可以简化为：
Figure PCTCN2020090520-appb-000090
其中，
Figure PCTCN2020090520-appb-000091
加速度计采样输出的均值，f b为加速度计的真实加速度值，
Figure PCTCN2020090520-appb-000092
为加速度计的常值漂移，
Figure PCTCN2020090520-appb-000093
为白噪声随机误差。
Figure PCTCN2020090520-appb-000094
主要是加速度计逐次启动的重复性误差，同样可以用随机常数表示，其误差模型为：
Figure PCTCN2020090520-appb-000095
定义加速度计的零偏误差为：
Figure PCTCN2020090520-appb-000096
5：双位置+卡尔曼算法的流程设计
对状态方程(4.2)和量测方程(4.4)与(4.8)离散化，得到GMD静基座下对准的随机系统状态空间模型：
Figure PCTCN2020090520-appb-000097
式(5.1)中，X k是公式(4.1)所示的12×1维的状态向量(式(4.1)中分别为：速度误差δv n、捷联惯导数学平台失准角φ n、高温陀螺常值漂移
Figure PCTCN2020090520-appb-000098
和高温加速度计常值零偏
Figure PCTCN2020090520-appb-000099
四个矢量每一个包含三轴分量，一共为12个)，Z k是速度量测Z v与角速率量测Z ω组成的量测向量；Φ k/k-1是12×1维的状态一步转移矩阵F的离散化，卡尔曼是递推的，因此，k-1是上一时刻，k是对k-1的一步递推时刻，Γ k/k-1是系统噪声分配矩阵、H k是量测矩阵，W k-1是系统噪声向量，V k是量测噪声向量，包含速度量测噪声与角速率量测噪声，W k-1与V k是互不相关的零均值的高斯白噪声向量序列，有：
Figure PCTCN2020090520-appb-000100
Q k和R k分别称为系统噪声和量测噪声的方差矩阵，在卡尔曼滤波中要求它们分别是已知的非负定阵和正定阵，δ kj是Kronecker(克罗内克)δ函数，当k≠j时，δ kj＝0，当k＝j时，δ kj＝1。
GMD精对准的离散卡尔曼滤波方程可划分为五个基本公式，如下：
①状态一步预测方程
Figure PCTCN2020090520-appb-000101
②一步预测均方误差方程
Figure PCTCN2020090520-appb-000102
③滤波增益方程
Figure PCTCN2020090520-appb-000103
④状态估值方程
Figure PCTCN2020090520-appb-000104
⑤状态估计均方误差方程
P k/k＝(I-K kH k)P k/k-1          (5.7)
图7为卡尔曼滤波算法的流程图，从图中可以看出，卡尔曼滤波的算法流程可以划分为两个计算回路与两个更新过程，左侧为滤波计算回路，完成被估计状态量的迭代计算，右侧为增益计算回路，完成卡尔曼增益的计算；虚线的上下构成了两个更新过程，在时间更新内，完成状态一步预测
Figure PCTCN2020090520-appb-000105
与均方误差一步预测P k/k-1，完成时间更新之后，此时如果没有量测数据，则一步预测值将作为状态的最优估计输出，在GMD转位过程，采用零速修正的速度量测与地球自转角速率约束的角速率量测都不具备，因此，在此过程无量测数据，最优估计值就是一步预测值，即：
Figure PCTCN2020090520-appb-000106
和P k＝P k/k-1，若量测数据值有效，即GMD处于转位前后的静止状态，且判断外部泥浆的扰动量小于设定值，此时开始量测更新，计算增益系数K k，得到最优状态估计
Figure PCTCN2020090520-appb-000107
同时计算此时的协方差矩阵P k/k，至此，完成了一个循环的最优状态估计。
基于卡尔曼最优估计的双位置对准算法采用了捷联惯导姿态更新算法与速度更新算法去实时更新载体的角运动与线运动，采用基于零速和地球自转角速率修正算法进行量测更新和最优估计。因此，最优估计精度与转位的精度无关，也无需知道转位机构的准确位置，这在工程实际中是非常有益的，避免了复杂止档结构的设计，也避免了使用耐高温的测角机构。这是本发明卡尔曼算法+双位置对准方法的特点和优势。
在量测更新过程中，需要求解高维数矩阵逆运算，从而获得卡尔曼滤波增益系数，为了降低运算量，常常采用序贯滤波(Sequential Kalman Filter)， 分别求解由速度量测Z v与地球自转角速率量测Z ω组成的量测矩阵。
GMD双位置精对准采用序贯处理的流程如图8所示。图8中的Z k有效判读，就是判读量测的数据有效性(公式(4.4)和(4.8))，即设定敏感速度或者敏感角速率的判据，去判读此时的钻铤是否处于静止状态或者是否保证其微小的扰动不影响对准的精度。状态变量完成时间更新后，当GMD探管处于静止或者微小扰动状态时，通过采集到的一段时间内的加速度计与陀螺仪的数据，自动判断观测量是否有效，按照序贯处理，分别完成速度量测Z v更新与角速率量测Z ω更新，计算卡尔曼增益，实现X、Y水平陀螺仪常值漂移误差最优估计与Z轴陀螺仪常值漂移误差估计(陀螺仪常值漂移误差的最优估计体现在状态矩阵X中包含的陀螺仪与加速度计漂移误差
Figure PCTCN2020090520-appb-000108
和
Figure PCTCN2020090520-appb-000109
)，最终完成姿态与方位失准角的最优估计。
量测方程有效下的最优估计的最终结果是式(5.6)；式(5.7)是估计后对估计效果的评价。式(5.3)到式(5.7)是估计的过程，是一个递推过程。
GMD系统检测到停钻寻北指令后，开启寻北(初始对准)模式，卡尔曼双位置对准算法基本流程如下：
1)在初始位置1，采用解析法粗对准算法在20s内完成粗对准；
2)以粗对准的水平姿态角与方位角作为卡尔曼滤波的初值，在位置1进行130s的精对准与惯性仪表的测漂，估计惯性仪表误差与失准角误差，然后以本次对准的结果作为初值进入导航状态；
东北天地理坐标系下，定义的水平姿态角：即为俯仰角和横滚角，对应钻井测量，对应的是井斜角和工具面角；定义的方位角，即为东北天下的方位角，对应钻井测术语，就是方位角或者和地理北向的夹角；
3)保证转位角速率小于Z轴陀螺仪最大测量量程的前提下，在20s内完成180°位置转动，转至位置2，同时更新姿态、速度导航数据；180°为优选，但是本发明并非只适用于180°转位，而是适用于任意转位；
4)在位置2进行130s的精对准，估计水平姿态与方位误差角并完成惯性仪表的测漂；测漂方式本领域有多种方法实现，这里不做赘述。
整个对准过程可以在约300s内完成，流程如图9所示。
精对准的流程具体为：
步骤1：进行姿态和速度更新；
以粗对准的俯仰角、横滚角、航向角(对应钻井的井斜角、工具面角、方位角)为初值，采用导航算法，进行速度更新和姿态更新；
1.1姿态更新的算法为：
为了更为简单的理解姿态更新与速度更新，这里列出其基本的算法，实际上，作为导航算法，姿态更新与速度更新是现有技术，这里给出一般性的物理数学方法实现：
四元数法：四元数是一种数学方法，在捷联惯导算法中，它被用来是描述坐标系变换关系和求解姿态矩阵的方便工具。
当刚体绕定点运动的欧拉一次转动定理可知，刚体由一位置到另一位置的有限转动，可以绕通过定点的某一轴转动某一角度的一次转动实现，且此一次转动可用如下单位四元数表示：
Figure PCTCN2020090520-appb-000110
四元数中的q中的角度α表示一次转动的角度，矢量ξ表示一次转动的转轴方位，并以ξ的指向按照右手法则作为转角α的正向。
四元数与姿态矩阵
Figure PCTCN2020090520-appb-000111
的关系，
Figure PCTCN2020090520-appb-000112
因此，已知载体转动的四元数，q 0、q 1、q 2、q 3，既可以求得载体坐标系到导航坐标系的变换矩阵
Figure PCTCN2020090520-appb-000113
从而可以进行捷联惯导系统的导航计算。
通过载体系b系测量得到的角速率
Figure PCTCN2020090520-appb-000114
建立的四元数微分方程
Figure PCTCN2020090520-appb-000115
实时获取载体的角速率矢量，就可以求取四元数，根据公式(a)，即可 获得载体的姿态方位信息，θ、γ、
Figure PCTCN2020090520-appb-000116
在求解公式(b)时，属于微分方程，需要获取四元数的初值，q 0(0)、q 1(0)、q 2(0)、q 3(0)，通过粗对准对准获取的方位姿态初值定义为：θ 0、γ 0、
Figure PCTCN2020090520-appb-000117
可以求取初始四元数为：
Figure PCTCN2020090520-appb-000118
通过递推求解四元数微分方程(b)，即可不断求取并更新载体的四元数，从而求取载体的姿态转换矩阵，从而实时计算出载体的姿态方位信息，θ、γ、
Figure PCTCN2020090520-appb-000119
这里的载体，就是需要GMD去测量的钻铤组件。
1.2速度更新的算法为：
速度微分方程即比力方程，是惯性导航解算的基本关系式
Figure PCTCN2020090520-appb-000120
式中g n＝[0 0 -g] T，为重力加速度在导航坐标系中的投影。
式中，f b是指加速度计实时量测得到的载体坐标系b系下的三分量值。式(5.8)中各参数均为向量或矢量。
Figure PCTCN2020090520-appb-000121
表示b系相对于i系的旋转角速率在b系的分量，
Figure PCTCN2020090520-appb-000122
表示n系相对于i系的旋转角速率在n系的分量，且
Figure PCTCN2020090520-appb-000123
Figure PCTCN2020090520-appb-000124
其中v E、v N为东、北向速度；L、h为纬度和高度；
ω ie为地球自转角速率。
已知纬度L，子午圈曲率半径R M和卯酉圈曲率半径R N可按下式计算：
Figure PCTCN2020090520-appb-000125
Figure PCTCN2020090520-appb-000126
CGCS2000椭球标准或WGS-84椭球标准的定义的扁率f。
步骤2：进行卡尔曼滤波；具体的算法划分为时间更新和量测更新两部分；
2.1姿态更新：将1.1姿态更新算法中更新的四元数，代入到姿态转移矩阵
Figure PCTCN2020090520-appb-000127
中，用于更新卡尔曼状态方程(4.2)中的F矩阵和W矩阵，从而实现卡尔曼的姿态更新。
b系与IMU(惯性测量单元)固联，随载体转动，原点位于IMU位置的敏感中心，用ox by bz b表示，用姿态矩阵
Figure PCTCN2020090520-appb-000128
表示b系与n系之间的角位置关系，导航坐标系与载体坐标系的姿态转移矩阵为：
Figure PCTCN2020090520-appb-000129
2.2时间更新：具体的更新方程式为状态一步预测方程和一步预测均方误差方程；
状态一步预测方程(5.3)：
Figure PCTCN2020090520-appb-000130
一步预测均方误差方程(5.4)：
Figure PCTCN2020090520-appb-000131
Φ k/k-1是12×1维的状态一步转移矩阵F的离散化、Γ k/k-1是系统噪声分配矩阵；
时间更新，只是计算状态变量在不同的陀螺仪与加速度计采集的实时数据下的12个状态量的更新，而此时的量测数据没有用到，量测更新，就是用量测数据去修正状态更新的误差，实现最优估计(方位和水平姿态、陀螺仪 与加速度计的漂移，即12个变量中的9个)。
2.3量测更新：
2.3.1先设置一个判据，判读量测数据值是否有效。可以通过判读钻铤是否处于静止状态或者外部扰动是否达到不影响对准精度的程度来判断量测数据值的有效性。量测数据值有效，才做量测更新，否则不作量测更新，只做时间更新，即：将时间更新中的状态一步预测方程或一步预测均方误差方程的更新结果作为卡尔曼滤波的输出(即，此时的水平姿态信息与方位信息，从公式(5.3)/(5.4)输出)。判读钻铤是否处于静止状态的设置具体可以是：设置观测到的敏感速度观测量(如加速度数值)或者敏感角速率观测量(如陀螺仪角速率的均方根值)，其值小于某一个量值时，执行量测更新；如果一直不满足，则不作量测更新，只做时间更新。外部扰动的判据可以是外部泥浆扰动量或振动传感器的量测值是否小于设定的阈值，若小于，则不影响对准精度，做量测更新，否则不做量测更新，只做时间更新。
2.3.2量测更新
量测方程(4.4)和(4.8)分别为基于零速约束的速度量测和基于地球自转角速率约束的角速率量测。
两种量测做序贯处理，即分别执行量测更新的公式(即公式(5.5)、(5.6)和(5.7))。
状态估值方程(5.6)为最终最优估计得到的卡尔曼滤波值，包括了初始对准的捷联惯导数学平台失准角φ n、陀螺常值漂移
Figure PCTCN2020090520-appb-000132
和加速度计常值零偏
Figure PCTCN2020090520-appb-000133
式(5.7)是估计后对估计效果的评价。
6：双位置卡尔曼对准算法的仿真试验与分析
设置初始位置为[116°E,40°N,100m]，高温惯性仪表的参数如表1，仿真流程与解析式双位置对准方法相同，在井斜角在0～90°范围，每5°取一位置做仿真，共19个位置，每个位置做40次Monte-Carlo仿真并取均方根值，仿真的井轨迹走向分为南北走向和东西走向，分析不同井斜角下的方位 对准误差，以及惯性仪表测漂的能力。
仿真一：井轨迹为南北走向，地理坐标系下的竖直井姿态[0°,0°,0°]，水平井姿态为[90°,0°,0°]，图10为失准角误差曲线，图11分别为陀螺仪与加速度计的常值漂移估计误差。
从图10可以看出，对于南北走向的井轨迹，在不同的井斜角下，方位测量精度基本保持不变，相关的机理分析类似于解析双位置对准，即南北走向时水平轴陀螺仪始终可以被转位机构调制，其常值漂移始终可观测，方位对准精度主要是取决于陀螺仪的角度随机游走。图10中每个位置都进行了40次Monte-Carlo仿真并取均方根值，计算从竖直井到水平井全姿态对准的方位失准角3σ标准方差为0.0576°，完全满足方位测量精度1°的设计要求。
仿真二：井轨迹为东西走向，地理坐标系下的竖直井姿态[0°,0°,90°]，水平井姿态为[90°,0°,90°]，以下分别从竖直井段、小井斜角、大井斜角下的对准精度与测漂能力进行仿真，最后得出在不同井斜角和不同方向下的对准精度与测漂能力仿真结论。
1)竖直井段仿真分析，设置初始姿态角为[0°,0°,90°]。
图12为一次仿真的失准角曲线，图13为加速度计(b)与陀螺仪(a)的常值漂移估计误差曲线，180°转位结束后，惯性仪表常值漂移误差迅速消除，由此也消除了水平姿态与方位的对准误差，最终一次仿真的结果显示，最终的方位失准角估计误差为-0.1°，失准角只与惯性仪表的随机漂移误差相关。
2)东西向井斜段仿真分析
在双位置解析对准仿真实验中，图4显示，当井斜角大于10°时，方位对准精度误差就超过了1°的设计指标。本次仿真，分别设置小井斜角15°，即初始姿态角为[15°,0°,90°]，以及大井斜角70°即初始姿态角为[70°,0°,90°]，20次Monte-Carlo仿真结果如图14(a)和14(b)所示。
图14中可以看出，无论在小井斜角和大井斜角下，转位180°后姿态与方位失准角误差都能够快速收敛，在15°小井斜角下，对准结束的方位失准 角均值为-0.0072°，3σ标准方差值为0.4°；在70°大井斜角下，对准结束方位失准角均值为0.1°，3σ标准方差值为0.9°，均满足1°的方位精度要求。
图15(a)和(b)给出了70°大井斜角下的惯性仪表的漂移估计的一次仿真结果，最终对准结束时，陀螺仪(对应图a)的常值漂移估计误差是[0.01,-0.02,-0.05]deg/h,加速度计(对应图b)的常值漂移估计误差是[4.6,-0.5,-0.05]ug。在70°大井斜角下，卡尔曼最优估计仍然能够较准确的估计惯性仪表的常值漂移。因此，本文设计的算法在当前高温陀螺仪存在2°/h较大的重复性误差情况下，仍然能够实现70°大井斜角东西走向的方位误差小于1°。
3)全井斜角下的方位精度分析，仿真设置井斜角在0～90°范围，每隔5°井斜角下做一次仿真，每个位置包含40次Monte-Carlo仿真，对准结束时取40个方位失准角数据的均方根值。
图16可以得出，采用本文提出的双位置卡尔曼+基于零速的速度量测以及基于地球自转角速率约束的角速率量测的最优估计，在东西走向井轨迹工况，当井斜角小于70°时，能保持方位对准精度优于1°，在完全水平井段，仍然能够实现优于5°的方位测量精度，其结果远远优于图4所示的双位置解析法对准的精度。
从图17也可以看出，Z轴陀螺仪的漂移误差在竖直井段(0°)到东西向大井斜角(75°)段下，都能够保证优于0.2deg/h的估计精度，在接近水平井(90°)时，估计精度变差，但是也能保证1deg/h的估计精度，因此，采用本发明的方法，可以非常好的估计竖直井段到水平井段下X/Y陀螺仪的漂移误差，并能够在满足在东西向水平井方向大井斜角下Z轴陀螺仪的漂移误差估计精度。
本发明多位置+转位置捷联解算+卡尔曼+零速修正的速度量测和地球自转角速率约束的角速率量测的对准方法，尤其适用于采用哥氏振动陀螺仪的捷联惯导系统。哥氏振动陀螺仪的精度主要取决于谐振子的加工精度、各项 同性均匀性以及控制电路精度，但受加工工艺等实际影响，谐振子的加工精度及材质的均匀性无法达到完美的程度，这就必然会造成谐振式陀螺仪角速率估计存在误差，造成捷联惯导系统方位对准误差。本发明的方法针对陀螺仪尤其是哥氏振动陀螺仪的漂移误差，同时采用零速修正的速度量测和地球自转角速率约束的角速率量测来进行量测更新，并结合转位过程的捷联解算算法，能够实现陀螺仪漂移误差的最优估计，从而提升GMD系统的方位测量精度。
本发明方法应用在惯性导航系统，惯性导航系统包括三轴陀螺仪及三轴加速度计、减振器，陀螺仪与减振器固联；三轴陀螺仪互相呈90度或其他角度设置。惯性导航系统为捷联惯导系统。
一种姿态测量方法的应用，将测量方法应用于哥氏振动陀螺仪的寻北过程中，以实现陀螺仪的初始对准。哥氏振动陀螺仪应用于随钻测量系统中。
本发明的姿态测量方法还可应用于多点陀螺罗盘随钻测量系统或多点陀螺罗盘有缆测量系统或具有零速修正能力的连续导航测量系统中，以实现地下井的姿态测量。
以上对本申请实施例所提供的一种姿态测量方法，进行了详细介绍。以上实施例的说明只是用于帮助理解本申请的方法及其核心思想；同时，对于本领域的一般技术人员，依据本申请的思想，在具体实施方式及应用范围上均会有改变之处，综上所述，本说明书内容不应理解为对本申请的限制。如在通篇说明书及权利要求书当中所提及的“包含”、“包括”为一开放式用语，故应解释成“包含/包括但不限定于”。“大致”是指在可接受的误差范围内，本领域技术人员能够在一定误差范围内解决所述技术问题，基本达到所述技术效果。应当理解，本文中使用的术语“和/或”仅仅是一种描述关联对象的关联关系，表示可以存在三种关系，例如，A和/或B，可以表示：单独存在A，同时存在A和B，单独存在B这三种情况。另外，本文中字符“/”，一般表示前后关联对象是一种“或”的关系。
上述说明示出并描述了本申请的若干优选实施例，应当理解本申请并非 局限于本文所披露的形式，不应看作是对其他实施例的排除，而可用于各种其他组合、修改和环境，并能够在本文所述申请构想范围内，通过上述教导或相关领域的技术或知识进行改动。而本领域人员所进行的改动和变化不脱离本申请的精神和范围，则都应在本申请所附权利要求书的保护范围内。

Claims (14)

  1. 一种姿态测量方法，所述方法用于捷联惯导系统，其特征在于，采用在多个位置分别进行精对准的方法对陀螺仪重复性漂移进行抑制；
    所述方法的步骤包括：
    S1、以陀螺仪的当前姿态数据和速度数据作为第一初值，在第一位置进行第一次精对准；
    S2、捷联惯导系统转位至第n位置，在转位过程中根据第n-1次精对准的结果进行姿态更新和速度更新；
    S3、以姿态更新和速度更新的结果为第n初值，在第n位置进行第n次精对准，完成捷联惯导系统的初始对准；
    其中，n从2开始做加1递增，重复步骤S2和S3，直至n＝k；k为所述方法所选用的位置的个数，且k大于等于2。
  2. 根据权利要求1所述的姿态测量方法，其特征在于，所述多个位置具体为双位置，即k＝2。
  3. 根据权利要求1所述的姿态测量方法，其特征在于，精对准采用卡尔曼算法实现。
  4. 根据权利要求3所述的姿态测量方法，其特征在于，采用卡尔曼算法进行精对准的内容包括：时间更新和/或量测更新；
    时间更新，根据系统采集的实时数据完成状态变量的更新，包含姿态更新和速度更新；
    量测更新，用量测数据修正状态更新的误差，实现最优估计；
    卡尔曼滤波采用零速修正的速度量测和地球自转角速率约束的角速率量测进行量测更新和最优估计，以消除陀螺仪漂移误差。
  5. 根据权利要求4所述的姿态测量方法，其特征在于，量测更新的步骤包括：
    1)判断量测数据值是否有效，若有效，进入2)，否则，不进行更新，将时间更新结果作为卡尔曼滤波的最终结果；
    2)根据量测数据值对状态更新结果进行修正，并根据修正结果和时间更新 结果，计算增益系数，得到最优状态估计。
  6. 根据权利要求5所述的姿态测量方法，其特征在于，判断量测数据值是否有效通过判断钻铤是否处于静止状态和/或判断外部扰动是否满足对准要求来实现；若钻铤处于静止状态和/或外部扰动满足对准要求，则判定量测数据值有效，否则判定量测数据值无效。
  7. 根据权利要求6所述的姿态测量方法，其特征在于，
    判断钻铤是否处于静止状态具体为：判断敏感速度观测量和/或敏感角速率观测量是否小于判定阈值，若是，则判定钻铤处于静止状态，否则不处于静止状态。
  8. 根据权利要求6所述的姿态测量方法，其特征在于，判断外部扰动是否满足对准要求具体为：判断外部泥浆的扰动量或振动传感器感应到的振动量是否小于设定的阈值；若是，则判定外部扰动量满足对准要求，否则不满足。
  9. 根据权利要求5所述的姿态测量方法，其特征在于，步骤2)的具体内容包括：分别求解由零速修正的速度量测Z v与地球自转角速率约束的角速率量测Z ω组成的量测矩阵，实现X、Y水平陀螺仪常值漂移误差最优估计与Z轴陀螺仪常值漂移误差估计，最终完成姿态与方位失准角的最优估计。
  10. 根据权利要求4所述的姿态测量方法，其特征在于，在时间更新时，完成状态一步预测与均方误差一步预测。
  11. 根据权利要求4所述的姿态测量方法，其特征在于，转位过程中的姿态更新采用四元数法进行更新。
  12. 根据权利要求1所述的姿态测量方法，其特征在于，所述测量方法还包括在第一位置的粗对准，并以粗对准的结果作为第一初值进行第一次精对准。
  13. 一种随钻测量系统，所述系统包括捷联惯导系统，所述捷联惯导系统包括三轴陀螺仪、三轴加速度计；其特征在于，所述捷联惯导系统采用权利要求1-12任一所述的姿态测量方法，抑制陀螺仪的重复性漂移误差，提高定向钻进的随钻测量的精度。
  14. 一种连续导航测量系统，所述系统包括捷联惯导系统，所述捷联惯导 系统包括三轴陀螺仪、三轴加速度计；其特征在于，所述捷联惯导系统采用权利要求1-12任一所述的姿态测量方法，抑制陀螺仪的重复性漂移误差，提高导航过程中的姿态测量精度。
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