CN109059961B - Error range analysis method for gyroscope measuring instrument - Google Patents

Error range analysis method for gyroscope measuring instrument Download PDF

Info

Publication number
CN109059961B
CN109059961B CN201810928750.3A CN201810928750A CN109059961B CN 109059961 B CN109059961 B CN 109059961B CN 201810928750 A CN201810928750 A CN 201810928750A CN 109059961 B CN109059961 B CN 109059961B
Authority
CN
China
Prior art keywords
noise
error
random
representing
angular rate
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201810928750.3A
Other languages
Chinese (zh)
Other versions
CN109059961A (en
Inventor
高爽
李玲玲
蔡晓雯
卢鑫
张若愚
纪少文
周文彬
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beihang University
Original Assignee
Beihang University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beihang University filed Critical Beihang University
Priority to CN201810928750.3A priority Critical patent/CN109059961B/en
Publication of CN109059961A publication Critical patent/CN109059961A/en
Application granted granted Critical
Publication of CN109059961B publication Critical patent/CN109059961B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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

Landscapes

  • Engineering & Computer Science (AREA)
  • Manufacturing & Machinery (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Gyroscopes (AREA)

Abstract

The invention discloses an error range analysis method for a gyroscope measuring instrument, which comprises the following steps: random noise analysis is carried out on the gyroscope by using an Allan variance method to obtain a random noise item and a random noise coefficient; establishing an azimuth error analysis model by using a random noise item and a random noise coefficient; and the azimuth angle error analysis model, the initial point position error range model and the well inclination angle error model form an error model in a gyroscope instrument continuous measurement mode, and the error model is superposed according to an error superposition principle and then subjected to multivariate normal distribution to obtain a borehole trajectory error range. The method utilizes an Allan variance method to analyze the random noise item of the gyroscope, selects random noise according to the Allan variance analysis result to perform error modeling, further calculates the error range of the well track position, and provides more reliable information for the fields of well collision prevention and the like.

Description

Error range analysis method for gyroscope measuring instrument
Technical Field
The invention relates to the technical field of oil inclination measurement, in particular to an error range analysis method for a gyroscope measuring instrument.
Background
Since the eighties of the last century, many oil fields in China begin to enter the middle and later development stages, exploration objects become increasingly complex, the difficulty in stable production of old oil fields is increased, and new technical problems of oil and gas exploration in new areas continuously appear. In order to improve the development efficiency of complex oil reservoirs such as thin oil reservoirs, hidden oil reservoirs and the like, the method fully exploits old oil fields, and the complex well structures such as directional wells, horizontal wells, branch wells, extended reach wells and the like are widely applied. The error range of the precise wellbore trajectory plays a key role in achieving the above goals.
The traditional inclinometer is mainly composed of a fluxgate and an accelerometer. The method based on the geomagnetic field has good impact resistance and interference resistance because no movable part is arranged in the system, has simple structure, small volume, light weight, quick start and low cost, becomes the first choice of a plurality of attitude measurement while drilling, but is easily interfered by the underground mineral magnetic field, and the measurement precision is seriously reduced. At present, the inertia measurement technology is applied to the field of inclination measurement more and more, and a mechanical gyroscope and an accelerometer are combined to realize borehole trajectory measurement. The existing fiber optic gyroscope has the advantages of high measurement precision, vibration resistance, strong magnetic interference resistance and the like, and is gradually developed in the field of inclination measurement. Therefore, the gyro strapdown inertial navigation system has wide application prospect in the field of borehole trajectory measurement.
An early model of borehole trajectory error range analysis was the WdW model, proposed by Wolff and deWardt in 1981, and the main subjects of this model study were instruments of magnetic compasses or free gyros. Williamson proposed a new model framework for MWD (measurement while drilling) based on the WdW model for the development of the drilling at that time, mainly including an error model for basic MWD measurement, a mathematical basis and simple data verification. Torgeir Torkildsen et al based on Williamson et al work, build an error model for a gyrometer that is applicable to most gyrometers. The model studies a new set of error terms and how these error terms contribute to the error ellipsoid in terms of sensor configuration and mode of operation. However, in a severe underground environment, main random noise items of different gyros are different in a gyro continuous measurement process, and a modeling process of a gyro instrument cannot be generally known.
Therefore, how to provide a method capable of analyzing the gyro random noise is a problem that needs to be solved by those skilled in the art.
Disclosure of Invention
In view of the above, the invention provides an error range analysis method for a gyro measurement instrument, which can effectively estimate the error range of a borehole trajectory in a continuous logging mode and provide reasonable analysis conditions for the application fields of borehole collision prevention and the like.
In order to achieve the purpose, the invention adopts the following technical scheme:
an error range analysis method for a gyroscopic measuring instrument, comprising the steps of:
s1: random noise analysis is carried out on the gyroscope by using an Allan variance method to obtain a random noise item and a random noise coefficient;
s2: establishing an azimuth error analysis model by using a random noise item and a random noise coefficient;
s3: and constructing an error model under a gyroscope instrument continuous measurement mode by using an azimuth angle error analysis model and combining an initial point position error range model and a well inclination angle error model, and after the error models are superposed according to an error superposition principle, performing multivariate normal distribution to obtain a borehole trajectory error range.
Further, S1: the method for analyzing the random noise of the gyroscope by using the Allan variance method comprises the following specific steps of:
s11: inputting the average angular rate sequence omega of the gyro and assuming the sampling interval is tauiThe number of angular rate samples is NiAnd obtaining an original angular rate sample by acquiring the output of the gyroscope under the condition that the cyclic condition i is 0
Figure BDA0001766022710000021
Figure BDA0001766022710000031
Wherein
Figure BDA0001766022710000032
For the original angular rate sample sequence, N0Representing the number of original angular rate samples;
s12: calculating a sampling interval tau from the original angular rate sample sequence or the new sampling point sequenceiAllan variance of time correspondences
Figure BDA0001766022710000033
S13: the cyclic condition is added with 1, i is i +1, and the sampling interval is doubled with taui＝2τi-1The number of angular rate samples is reduced by half Ni＝[Ni-1/2]Calculating number average between adjacent odd-even serial number angular rate samples to obtain a new sampling point sequence;
s14: judging the number N of angular rate samplesiIf the value is less than 3, if so, executing S15, otherwise, returning to S12;
s15: drawing sampling interval tauiVariance with corresponding Allan
Figure BDA0001766022710000034
And the Allan variance obtained from each sampling interval
Figure BDA0001766022710000035
And performing curve fitting to obtain a random noise item and a random noise coefficient.
Further, Allan variance
Figure BDA0001766022710000036
The calculation formula of (2) is as follows:
Figure BDA0001766022710000037
wherein K represents the number of the current sample sequence,
Figure BDA0001766022710000038
respectively representing the K +1 th value and the K-th value of the current sample sequence,
Figure BDA0001766022710000039
further, the Allan variance is obtained according to each sampling interval
Figure BDA00017660227100000310
The specific steps of performing curve fitting to obtain the random noise coefficient are as follows:
the fitting formula is:
Figure BDA00017660227100000311
wherein,
Figure BDA00017660227100000312
representing the variance of the quantization noise alan,
Figure BDA00017660227100000313
representing the angle random walk noise alan variance,
Figure BDA00017660227100000314
representing the null-bias instability noise alan variance,
Figure BDA00017660227100000315
representing the angular rate random walk noise alan variance,
Figure BDA00017660227100000316
representing the rate ramp noise Allan variance,. tau.representing the sampling time, A-2,A-1,A0,A1,A2Respectively with the quantization noise factor QcoeAngle random walk noise figure NcoeZero-bias instability noise coefficient BcoeAngular rate random walk noise figure KcoeSum rate ramp noise factor Rcoe(ii) related;
according to the curve chart and the Allan variance
Figure BDA0001766022710000041
Fitting the formula (2) to obtain A-2,A-1,A0,A1,A2(ii) a And obtaining the random noise coefficient according to the following formula:
Figure BDA0001766022710000042
Figure BDA0001766022710000043
Figure BDA0001766022710000044
Figure BDA0001766022710000045
Figure BDA0001766022710000046
wherein h represents hours, (°) represents degrees, (") represents angular degrees.
Further, S2: the method for carrying out azimuth angle error analysis modeling by utilizing the random noise item and the random noise coefficient comprises the following specific steps:
s21: if the analysis result of S1 contains zero-bias instability noise item, the label of the zero-bias instability noise item is GB, and the error magnitude is the zero-bias instability noise coefficient BcoeThe propagation mode is S, and the zero-bias instability error weight function is:
Figure BDA0001766022710000047
wherein h isGB(i-1)An error weight function of the zero bias instability noise term of the last measurement segment, c represents the speed of the gyro in uniform motion, and delta DiRepresenting a distance traveled interval;
s22: if the analysis result of S1 contains the angle random walk noise term, the index of the angle random walk noise term is GN, and the error magnitude is the random coefficient N of the angle random walkcoeThe propagation mode is S, and the angle random walk error weight function is:
Figure BDA0001766022710000048
wherein h isGN(i-1)An error weight function of the random walk noise term of the previous measurement section angle, c represents the speed of the gyro in uniform motion, and delta DiRepresenting a distance traveled interval;
s23: if the analysis result of S1 contains the angular rate random walk noise term, the index of the angular rate random walk noise term is GK, and the error magnitude is the coefficient K of the angular rate random walk noisecoeThe propagation mode is S, and the angular rate random walk error weight function is:
Figure BDA0001766022710000051
wherein h isGK(i-1)Representing the error weight function of the random walk noise term of the last measured segment angular rate, c representing the speed of the gyro in uniform motion, and delta DiRepresenting a distance traveled interval;
s24: if the S1 analysis result contains the rate ramp noise item, the rate ramp noise item is marked as GR, and the error magnitude is the rate ramp noise coefficient RcoeThe propagation mode is S, and the rate ramp weight function is:
Figure BDA0001766022710000052
wherein h isGR(i-1)Representing the error weight function of the slope noise term of the previous segment rate, c representing the speed of the uniform motion of the gyroscope, and Delta DiRepresenting a distance traveled interval;
the propagation mode S represents systematic propagation;
and obtaining an azimuth angle error analysis model through the error magnitude, the propagation mode and the weight function of each noise item.
According to the technical scheme, compared with the prior art, the invention discloses an error range analysis method for a gyro measuring instrument, random noise of a gyro is analyzed by using an Allan variance method, random noise is selected according to the result of the Allan variance analysis to perform error modeling, the error range of a borehole track position is further calculated, and more reliable information is provided for the fields of borehole collision prevention and the like. The method can select different random noises to model according to the characteristics of different gyro instruments, and can enable the model output, namely the borehole trajectory error ellipsoid, to be more accurate.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
Fig. 1 is a flow chart of random noise analysis by using an alan variance method according to the present invention.
Fig. 2 is a diagram showing the output result of analyzing the random error noise of the fiber-optic gyroscope by using an Allan variance method under the vibration condition provided by the invention, wherein the sampling interval is 0.1s, and the acquisition time is 3000 s.
Fig. 3 is a graph showing the variation of the difference between the error ellipsoid and the ISCSSA model.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention discloses an error range analysis method for a gyroscope measuring instrument, which specifically comprises the following steps with reference to the attached figure 1:
s11: the input to the Allan variance is the mean angular rate sequence of the gyro Ω, assuming a sampling interval of τiAngular rate samplesNumber is NiAnd obtaining an original angular rate sample by acquiring the output of the gyroscope under the condition that the cyclic condition i is 0
Figure BDA0001766022710000061
Wherein
Figure BDA0001766022710000062
Original angular rate sample sequence, N0Representing the number of original angular rate samples;
s12: calculating the sampling interval tau according to the obtained original angular rate sample sequence0Allan variance of time, angular rate samples
Figure BDA0001766022710000063
Namely, it is
Figure BDA0001766022710000064
S13: the loop condition is increased by 1, i.e. 1, and the sampling interval is doubled, i.e. τ1＝2τ0，N1＝[N0/2]Wherein, [.]Representing rounding, arithmetic averaging between adjacent parity angular rates, i.e.
Figure BDA0001766022710000071
Constitute a new sampling time interval of tau1Of the average angular rate (new sequence of sampling points), i.e.
Figure BDA0001766022710000072
S14: it is apparent that the length of the new sequence of sample points is halved (possibly by one data difference), and the sample interval is calculated as τ1Allan variance of time
Figure BDA0001766022710000073
Figure BDA0001766022710000074
S15: the cycle condition is increased by 1, and the sampling interval is again doubled, i.e. τ2＝2τ1，N2＝[N1/2]Wherein, [.]Meaning rounding, averaging between adjacent parity numbers, i.e.
Figure BDA0001766022710000075
Constitute a new sampling time interval of tau2Of average angular rate, i.e.
Figure BDA0001766022710000076
S16: calculating the sampling interval tau according to the obtained new sampling point sequence2Allan variance of time, angular rate samples
Figure BDA0001766022710000077
Figure BDA0001766022710000078
S17: so repeatedly doubling the sampling interval, i.e. taui＝2τi-1Number of angular rate samples Ni＝[Ni-1/2]Up to the number of angular rate samples NiLess than 3, the cycle is stopped and the average angular rate obtained is
Figure BDA0001766022710000079
S18: a series of point pairs are now obtained
Figure BDA00017660227100000710
Drawing a curve graph of the point pair, and carrying out curve fitting according to a formula (1) to obtain each coefficient in the formula (1);
Figure BDA00017660227100000711
wherein,
Figure BDA00017660227100000712
representing the variance of the quantization noise alan,
Figure BDA00017660227100000713
representing the angle random walk noise alan variance,
Figure BDA00017660227100000714
representing the null-bias instability noise alan variance,
Figure BDA00017660227100000715
representing the angular rate random walk noise alan variance,
Figure BDA00017660227100000716
representing the rate ramp noise Allan variance,. tau.representing the sampling time, A-2,A-1,A0,A1,A2Respectively with the quantization noise factor QcoeAngle random walk noise figure NcoeZero-bias instability noise coefficient BcoeAngular rate random walk noise figure KcoeSum rate ramp noise factor Rcoe(ii) related;
then according to the coefficient A in the formula (1)-2,A-1,A0,A1,A2(ii) a The random noise figure is obtained by combining the following formula:
Figure BDA0001766022710000081
Figure BDA0001766022710000082
Figure BDA0001766022710000083
Figure BDA0001766022710000084
Figure BDA0001766022710000085
wherein h represents hours, (°) represents degrees, (") represents angular degrees.
It should be noted that the several noise terms are independent from each other, if the several noise terms are included in the gyro output, the total lian variance of the gyro output can be represented by adding the several terms, if a is related to the coefficient of the corresponding noise term-2,A-1,A0,A1,A2Approximately 0, the noise can be ignored, i.e., the model does not include the noise.
Further, S11 to S18 are sequential, but S21 to S24 are not sequential.
And carrying out azimuth angle error analysis modeling by utilizing random noise terms and random noise coefficients, wherein only noise terms related to time in random noise, namely angle random walk noise, angle rate random walk noise, rate slope noise and zero-bias instability noise, are considered in the modeling process.
S21: if the analysis result of S1 contains zero-bias instability noise item, the label of the zero-bias instability noise item is GB, and the error magnitude is the zero-bias instability noise coefficient BcoeThe propagation mode is S, and the zero-bias instability error weight function is:
Figure BDA0001766022710000086
wherein h isGB(i-1)The error weight function of the noise term for the previous segment.
The derivation process of the zero-bias instability error weight function is as follows:
(1) assuming that the running process of the instrument is constant-speed running and the speed is c, the running distance interval delta D isiThen, the gyro zero bias instability noise coefficient BcoeThe amount of change in the resulting azimuth angle error can be represented by the formula (S2-1):
Figure BDA0001766022710000091
wherein, Delta AiIs the azimuth error, Δ A, of the current measurement segmenti-1Is the azimuth error of the last measurement section, BcoeThe error magnitude of the zero-bias instability random noise term, namely the zero-bias instability noise coefficient analyzed by the S1,
the azimuthal error at a certain measurement point due to gyro zero-bias instability can be obtained from the formula (S2-2).
Figure BDA0001766022710000092
(2) And determining an error weight function of zero bias instability according to the expression of the azimuth angle error variation, as shown in formula (7).
S22: if the analysis result of S1 contains the angle random walk noise term, the index of the angle random walk noise term is GN, and the error magnitude is the random coefficient N of the angle random walkcoeThe propagation mode is S, and the angle random walk error weight function is:
Figure BDA0001766022710000093
the derivation process of the angle random walk error weight function is as follows:
(1) assuming that the running process of the instrument is constant-speed running and the speed is c, the running distance interval delta D isiThen, the random walk coefficient N is calculated according to the anglecoeThe amount of change in the resulting azimuth angle error can be represented by the formula (S2-3):
Figure BDA0001766022710000094
wherein, Delta AiIs the azimuth error, Δ A, of the current measurement segmenti-1Is the azimuth error of the last measurement section, NcoeIs an angleAnd the magnitude of the error of the random walk random noise term is the coefficient of the angular random walk noise term analyzed by S1.
The azimuthal error at a certain measuring point due to the random angular walk can be obtained by the formula (S2-4).
Figure BDA0001766022710000101
(2) And determining a weight function of the error term of the zero offset stability by the expression of the azimuth angle error variation, as shown in formula (8).
S23: if the analysis result of S1 contains the angular rate random walk noise term, the index of the angular rate random walk noise term is GK, and the error magnitude is the coefficient K of the angular rate random walk noisecoeThe propagation mode is S, and the angular rate random walk error weight function is:
Figure BDA0001766022710000102
the angular rate random walk error weight function derivation formula is as follows:
(1) assuming that the running process of the instrument is constant-speed running and the speed is c, the running distance interval delta D isiThen randomly walk K by anglecoeThe amount of change in the resulting azimuth angle error can be represented by the formula (S2-5):
Figure BDA0001766022710000103
wherein, Delta AiIs the azimuth error, Δ A, of the current measurement segmenti-1Is the azimuth error of the last measurement section, KcoeThe magnitude of the error of the angular rate random walk noise term, i.e., the angular rate random walk noise coefficient analyzed at S1.
The azimuthal error at a certain measurement point due to random walk of angular velocity can be obtained by the formula (S2-6):
Figure BDA0001766022710000104
(2) and determining a weight function of the error term of random walk of the rate according to the expression of the azimuth angle error variation, as shown in the formula (9):
s24: if the S1 analysis result contains the rate ramp noise item, the rate ramp noise item is marked as GR, and the error magnitude is the rate ramp noise coefficient RcoeThe propagation mode is S, and the rate ramp weight function is:
Figure BDA0001766022710000111
the derivation process of the rate ramp weight function is as follows:
(1) assuming that the running process of the instrument is constant-speed running and the speed is c, the running distance interval delta D isiThen, by a rate ramp RcoeThe amount of change in the resulting azimuth angle error can be represented by the formula (S2-7):
Figure BDA0001766022710000112
the azimuthal error at a certain point due to the rate ramp can be obtained from the equation (S2-8).
Figure BDA0001766022710000113
(2) The weight function of the error term of the rate ramp is determined by the expression of the azimuth error variation, as shown in equation (10).
The referred propagation mode S represents systematic propagation.
It should be noted that an error weight function of a certain term is a transfer formula between an error magnitude of a certain error source and an azimuth error, and after an expression of the azimuth error is known, the weight function can be derived, which is a superposition process.
The azimuth error analysis modeling mainly comprises an error term, error identification, an error magnitude, an error weight function and an error propagation mode, so that an azimuth error analysis model can be obtained through S21-S24.
For convenience of viewing, an azimuth angle error analysis model obtained by using zero-offset instability noise, angle random walk noise, angle rate random walk noise and rate slope noise is summarized as table 1;
TABLE 1 Azimuth angle error analysis model under gyro instrument continuous measurement mode
Figure BDA0001766022710000121
S3: the uncertainty model in the continuous measurement mode of the gyroscope includes an azimuth error analysis model, an initial point position error range model and a well deviation angle error model, wherein the initial point position error range and the well deviation angle error model belong to the prior art and are not described herein again.
In the field of borehole trajectories, it is generally assumed that borehole trajectory position errors are normally distributed, and then, after an uncertainty model in a gyro instrument continuous measurement mode is superimposed according to an error superposition principle, a three-dimensional borehole trajectory error range can be obtained according to multivariate normal distribution, and a calculation process of the three-dimensional borehole trajectory error range can be referred to in patent CN 201510303420.1.
(1) The data output from fig. 2 were analyzed by the alan variance method, and the coefficients of the random noise term of the fiber optic gyroscope under random vibration conditions are shown in table 2:
TABLE 2 fitting noise term coefficients under vibration conditions
Fitting noise terms Allan variance method fitting result
Qcoe 3.110160
Ncoe 0.074009
Bcoe 3.679420
Kcoe 14.200481
Rcoe 15.621677
(2) Uncertainty analysis of borehole trajectory under vibratory conditions
And analyzing the inclination measurement data by using an ISCSWSA model and the improved model provided by the invention respectively to obtain an error ellipsoid at the corresponding measuring point. For both models, the error ellipsoid size is shown in table 3:
TABLE 3 error ellipsoid size comparison
Figure BDA0001766022710000131
From the data calculated in tables 2 and 3 and fig. 2 and 3, it can be seen that the magnitude of the error ellipsoid of the improved model under the random vibration condition is significantly larger than that of the error ellipsoid of the conventional ISCWSA model, and the difference is more obvious and can not be ignored.
The method analyzes the random noise item of the gyroscope by using an Allan variance method, selects random noise according to the result of the Allan variance analysis to carry out error modeling, further calculates the error range of the track position of the well, provides more reliable information for the fields of well collision prevention and the like, and solves the problem that the error analysis is inaccurate because a gyroscope continuous measurement model only considers zero-bias instability and angle random walk coefficients.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (4)

1. An error range analysis method for a gyroscopic measuring instrument, comprising the steps of:
s1: random noise analysis is carried out on the gyroscope by using an Allan variance method to obtain a random noise item and a random noise coefficient;
s2: establishing an azimuth error analysis model by using a random noise item and a random noise coefficient; the method comprises the following specific steps:
s21: if the analysis result of S1 contains zero-bias instability noise item, the label of the zero-bias instability noise item is GB, and the error magnitude is the zero-bias instability noise coefficient BcoeThe propagation mode is S, and the zero-bias instability error weight function is:
Figure FDA0003090475110000011
wherein h isGB(i-1)For the last segment zero-bias instability noise termC represents the speed of the gyro in uniform motion, Δ DiRepresenting a distance traveled interval;
s22: if the analysis result of S1 contains the angle random walk noise term, the index of the angle random walk noise term is GN, and the error magnitude is the random coefficient N of the angle random walkcoeThe propagation mode is S, and the angle random walk error weight function is:
Figure FDA0003090475110000012
wherein h isGN(i-1)An error weight function of the random walk noise term of the previous measurement section angle, c represents the speed of the gyro in uniform motion, and delta DiRepresenting a distance traveled interval;
s23: if the analysis result of S1 contains the angular rate random walk noise term, the index of the angular rate random walk noise term is GK, and the error magnitude is the coefficient K of the angular rate random walk noisecoeThe propagation mode is S, and the angular rate random walk error weight function is:
Figure FDA0003090475110000013
wherein h isGK(i-1)Representing the error weight function of the random walk noise term of the last measured segment angular rate, c representing the speed of the gyro in uniform motion, and delta DiRepresenting a distance traveled interval;
s24: if the S1 analysis result contains the rate ramp noise item, the rate ramp noise item is marked as GR, and the error magnitude is the rate ramp noise coefficient RcoeThe propagation mode is S, and the rate ramp weight function is:
Figure FDA0003090475110000021
wherein h isGR(i-1)Error weight representing last segment rate ramp noise termFunction, c represents the speed of the gyro in uniform motion, Δ DiRepresenting a distance traveled interval;
the propagation mode S represents systematic propagation;
obtaining an azimuth error analysis model through the error magnitude, the propagation mode and the weight function of each noise;
s3: and constructing an error model under a gyroscope instrument continuous measurement mode by using an azimuth angle error analysis model and combining an initial point position error range model and a well inclination angle error model, and after the error models are superposed according to an error superposition principle, performing multivariate normal distribution to obtain a borehole trajectory error range.
2. The method for analyzing the error range of the gyroscopic measuring instrument as claimed in claim 1, wherein the step of S1: the method for analyzing the random noise of the gyroscope by using the Allan variance method comprises the following specific steps of:
s11: the average angular rate sequence omega of the gyro is input, assuming a sampling interval of tauiThe number of angular rate samples is NiAnd obtaining an original angular rate sample by acquiring the output of the gyroscope under the condition that the cyclic condition i is 0
Figure FDA0003090475110000022
Figure FDA0003090475110000023
Wherein
Figure FDA0003090475110000024
For the original angular rate sample sequence, N0Representing the number of original angular rate samples;
s12: calculating a sampling interval tau from the original angular rate sample sequence or the new sampling point sequenceiAllan variance of time correspondences
Figure FDA0003090475110000025
S13: adding 1, i to i +1 to the cycling conditions,doubling of sampling interval τi＝2τi-1The number of angular rate samples is reduced by half Ni＝[Ni-1/2]，[.]Expressing rounding, and performing arithmetic mean between adjacent odd-even serial number angular rate samples to obtain a new sampling point sequence;
s14: judging the number N of angular rate samplesiIf the value is less than 3, if so, executing S15, otherwise, returning to S12;
s15: drawing sampling interval tauiVariance with corresponding Allan
Figure FDA0003090475110000031
And the Allan variance obtained from each sampling interval
Figure FDA0003090475110000032
And performing curve fitting to obtain a random noise item and a random noise coefficient.
3. The method of claim 2, wherein the Allan variance is used as a measure of error range
Figure FDA0003090475110000033
The calculation formula of (2) is as follows:
Figure FDA0003090475110000034
wherein,<·>representing the averaging of the overall data, K represents the number of current sample sequences,
Figure FDA0003090475110000035
respectively representing the K +1 th value and the K-th value of the current sample sequence,
Figure FDA0003090475110000036
K＝1,2,3…Ni。
4.the method of claim 3, wherein the sampling interval τ is plottediVariance with corresponding Allan
Figure FDA0003090475110000037
And the Allan variance obtained from each sampling interval
Figure FDA0003090475110000038
The specific steps of performing curve fitting to obtain a random noise item and a random noise coefficient are as follows:
the fitting formula is:
Figure FDA0003090475110000039
wherein,
Figure FDA00030904751100000310
representing the variance of the quantization noise alan,
Figure FDA00030904751100000311
representing the angle random walk noise alan variance,
Figure FDA00030904751100000312
representing the null-bias instability noise alan variance,
Figure FDA00030904751100000313
representing the angular rate random walk noise alan variance,
Figure FDA00030904751100000314
representing the rate ramp noise Allan variance,. tau.representing the sampling time, A-2,A-1,A0,A1,A2Respectively with the quantization noise factor QcoeAngle random walk noise figure NcoeZero-bias instability noise figureBcoeAngular rate random walk noise figure KcoeSum rate ramp noise factor Rcoe(ii) related;
according to the curve chart and the Allan variance
Figure FDA0003090475110000041
Fitting the formula (2) to obtain A-2,A-1,A0,A1,A2(ii) a And obtaining random noise coefficients of the terms according to the following formula:
Figure FDA0003090475110000042
Figure FDA0003090475110000043
Figure FDA0003090475110000044
Figure FDA0003090475110000045
Figure FDA0003090475110000046
wherein h represents hours, (°) represents degrees, (") represents angular degrees.
CN201810928750.3A 2018-08-15 2018-08-15 Error range analysis method for gyroscope measuring instrument Active CN109059961B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201810928750.3A CN109059961B (en) 2018-08-15 2018-08-15 Error range analysis method for gyroscope measuring instrument

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201810928750.3A CN109059961B (en) 2018-08-15 2018-08-15 Error range analysis method for gyroscope measuring instrument

Publications (2)

Publication Number Publication Date
CN109059961A CN109059961A (en) 2018-12-21
CN109059961B true CN109059961B (en) 2021-11-05

Family

ID=64686925

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201810928750.3A Active CN109059961B (en) 2018-08-15 2018-08-15 Error range analysis method for gyroscope measuring instrument

Country Status (1)

Country Link
CN (1) CN109059961B (en)

Families Citing this family (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111157019A (en) * 2020-01-06 2020-05-15 金陵科技学院 EMD-Allan-based micromechanical gyroscope signal analysis method
CN111400907A (en) * 2020-03-16 2020-07-10 中南大学 Unified modeling method for random errors of fiber-optic gyroscope
CN111397637B (en) * 2020-06-01 2020-09-04 湖南跨线桥航天科技有限公司 Gyroscope random walk error suppression method of biaxial rotation modulation type inertial navigation system
CN112683308A (en) * 2020-12-16 2021-04-20 湖南航天机电设备与特种材料研究所 Random noise estimation method and system for acceleration channel of high-precision rate offset frequency inertial measurement unit
CN112729266A (en) * 2020-12-22 2021-04-30 陕西航天时代导航设备有限公司 Analysis method for MEMS gyroscope random error

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8670964B2 (en) * 2009-10-15 2014-03-11 American Gnc Corporation Gyrocompass modeling and simulation system (GMSS) and method thereof
CN103674062A (en) * 2013-12-05 2014-03-26 广东电网公司电力科学研究院 Method to improve gyroscope measurement accuracy based on Allan variance and ARMA (Autoregressive moving average model) analysis
CN104881547A (en) * 2015-06-05 2015-09-02 北京航空航天大学 Method for analyzing errors of well tracks of directional wells
CN105041295A (en) * 2015-06-04 2015-11-11 北京航空航天大学 Inertia measurement method for well track measurement
CN107608065A (en) * 2017-10-18 2018-01-19 中国科学院光电技术研究所 Telescope automatic pointing correction method based on A LL AN variance analysis under motion platform

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8670964B2 (en) * 2009-10-15 2014-03-11 American Gnc Corporation Gyrocompass modeling and simulation system (GMSS) and method thereof
CN103674062A (en) * 2013-12-05 2014-03-26 广东电网公司电力科学研究院 Method to improve gyroscope measurement accuracy based on Allan variance and ARMA (Autoregressive moving average model) analysis
CN105041295A (en) * 2015-06-04 2015-11-11 北京航空航天大学 Inertia measurement method for well track measurement
CN104881547A (en) * 2015-06-05 2015-09-02 北京航空航天大学 Method for analyzing errors of well tracks of directional wells
CN107608065A (en) * 2017-10-18 2018-01-19 中国科学院光电技术研究所 Telescope automatic pointing correction method based on A LL AN variance analysis under motion platform

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
光纤陀螺随机游走系数的分析研究;宋凝芳等;《中国惯性技术学报》;20040815;第12卷(第4期);第34-38页 *
定向井轨迹误差模型研究;孟照魁等;《测井技术》;20160215;第40卷(第1期);第52-55页 *

Also Published As

Publication number Publication date
CN109059961A (en) 2018-12-21

Similar Documents

Publication Publication Date Title
CN109059961B (en) Error range analysis method for gyroscope measuring instrument
CN103776446B (en) A kind of pedestrian&#39;s independent navigation computation based on double MEMS-IMU
US10047600B2 (en) Attitude reference for tieback/overlap processing
CN100547352C (en) The ground speed testing methods that is suitable for fiber optic gyro strapdown inertial navigation system
CN101949710B (en) Rapid online dynamic calibration method for zero offset of GNSS (Global Navigation Satellite System) auxiliary MEMS (Micro Electro Mechanical Systems) inertial sensor
CN103114846B (en) A kind for the treatment of system afterwards of the deviational survey data based on optic fiber gyroscope inclinometer
US20160032709A1 (en) System and method for providing a continuous wellbore survey
CN105300379A (en) Kalman filtering attitude estimation method and system based on acceleration
CA2666291A1 (en) Downhole depth computation methods and related system
Torkildsen et al. Prediction of wellbore position accuracy when surveyed with gyroscopic tools
CN101109636B (en) Data processing method for optical fiber gyroscope north finding
CN103344260A (en) Initial alignment method of large azimuth misalignment angle of strapdown inertial navigation system based on RBCKF (rao-black-wellised cubature kalman filter)
Luo et al. A position loci-based in-motion initial alignment method for low-cost attitude and heading reference system
CN108225374A (en) A kind of Allan methods of analysis of variance of blending inheritance algorithm
CN102288177B (en) Strapdown system speed calculating method based on angular speed output
CN110672095A (en) Pedestrian indoor autonomous positioning algorithm based on micro inertial navigation
CN108121890A (en) A kind of navigation attitude information fusion method based on linear Kalman filter
CN105134171B (en) A kind of implementation method of the continuous inclination measurement system of two axles optical fibre gyro
CN113137977A (en) SINS/polarized light combined navigation initial alignment filtering method
Bochkati et al. Could cold atom interferometry sensors be the future inertial sensors?—First simulation results
CN114909608B (en) Non-excavation pipeline positioning method based on MIMU/mileage wheel/photoelectric speed measurement module combination
CN102221366B (en) Quick accurate alignment method based on fuzzy mapping earth spin velocity
CN115664380A (en) Thick tail measurement noise filtering model of near-bit measurement while drilling system and establishing method
CN115163030A (en) Well re-drilling processing method, device and system
CN103471594B (en) Based on the fine alignment algorithm of AHRS

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant