CN111207744B - Pipeline geographical position information measuring method based on thick tail robust filtering - Google Patents

Pipeline geographical position information measuring method based on thick tail robust filtering Download PDF

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CN111207744B
CN111207744B CN202010039909.3A CN202010039909A CN111207744B CN 111207744 B CN111207744 B CN 111207744B CN 202010039909 A CN202010039909 A CN 202010039909A CN 111207744 B CN111207744 B CN 111207744B
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pipeline
position information
strapdown
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CN111207744A (en
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李倩
赵显鹏
奔粤阳
赵玉新
陈立恒
吴磊
王洪星
戴平安
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Harbin Engineering University
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    • 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
    • G01C21/18—Stabilised platforms, e.g. by gyroscope
    • 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

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Abstract

The invention discloses a pipeline geographical position information measuring method based on thick tail robust filtering, and relates to a technology for measuring geographical position information of a pipeline. Specifically, an inertia/mileage wheel combined positioning system is formed by the MSINS and the mileage wheel, the system power device drives the system power device to run in a pipeline to acquire sensor data related to the pipeline trend, and strapdown inertia calculation and dead reckoning are respectively carried out; the difference value of the strapdown inertial calculation position and the dead reckoning position is used as measurement information, position measurement outlier information caused by the slip of a mileage wheel, the sliding fault and the failure of a pipeline motion constraint condition is filtered by a thick tail robust filter, meanwhile, a strapdown inertial calculation error is estimated, and the pipeline geographic position information is corrected and output, so that the system provides continuous and high-precision pipeline geographic position information.

Description

Pipeline geographical position information measuring method based on thick tail robust filtering
Technical Field
The invention relates to a method for measuring pipeline geographical position information, in particular to a method for measuring pipeline geographical position information based on thick tail robust filtering.
Background
Underground pipelines are important components of urban infrastructure, and pipelines for water supply, drainage, gas, heat supply and the like convey substances and energy for daily life of people, so that the underground pipelines are life lines for guaranteeing normal and orderly life of cities. However, as the operation time of the pipeline increases and the local geological structure changes, various environmental factors such as settlement, frost heaving and the like easily cause displacement and deformation of the in-service pipeline, so that a local pipe body generates large bending strain, and the pipeline failure problems such as pipeline instability or material damage and the like are caused in serious conditions, so that the structural integrity and the operation safety of the pipeline cannot be guaranteed. In addition, pipeline corrosion, failure of welding seam material and the like can also cause safety accidents such as pipeline leakage, explosion and the like. Therefore, the method has great significance for regularly detecting the running state of the pipeline and effectively preventing and maintaining accidents to guarantee the life and property safety of people. The measurement of the geographical position information of the pipeline is one of the key technologies for realizing the detection of the running state of the pipeline. The effects mainly comprise: 1. accurately measuring the relative displacement and deformation of the pipeline so as to determine whether the structural mechanics is normal or not; 2. the position of the pipeline defect part is accurately determined, so that maintenance operation is facilitated, and waste of manpower, material resources and financial resources caused by blind excavation is avoided.
The traditional underground pipeline positioning method mainly comprises an electromagnetic pipeline detector, a ground penetrating radar and the like. However, these methods often fail to accurately obtain the geographic location information of existing trenchless pipelines due to the influence of pipeline depth or pipeline material. Based on the outstanding measurement capability of the inertial navigation system and the completely autonomous and independent measurement principle, the micro inertial strapdown measurement system (MSINS) is used for measuring the geographic position information of the urban underground pipelines, so that the defects of the existing pipeline positioning method can be overcome, and the requirements of the geographic position information measurement of the urban underground pipelines on low cost, small size, universality and the like can be met. However, since MSINS uses miniature inertial measurement components, micro-mechanical (MEMS) gyroscopes and accelerometers, as its inertial measurement unit, and micro-mechanical gyroscope errors and stability are inferior to other types of gyroscopes, it is generally not suitable for use alone and needs external sensor assistance. In consideration of the special underground application environment of the pipeline, the combination positioning system formed by the MSINS and the mileage wheel is a feasible combination positioning mode. The position information provided by the mileage wheel is used as measurement information, and strapdown inertial calculation errors are estimated and corrected by using a filtering technology, so that the measurement precision of the geographical position information of the pipeline is effectively improved. However, when the odometer wheel runs in a pipeline, problems such as slipping or sliding faults often occur, and factors such as pipeline defects also cause the odometer wheel to generate non-pipeline motion model constraint actions such as jumping, and the above problems cause wild values in the position measurement information of the odometer wheel, so that the measurement noise distribution presents an obvious thick tail phenomenon. In the existing inertia/mileage wheel combined positioning system, the traditional kalman filtering technology is usually used to realize the filtering state estimation. However, the processing of the system noise and the measurement noise by the traditional kalman filtering algorithm is usually assumed to be white gaussian noise, which has obvious modeling error with the thick tail noise in the actual system, thereby reducing the measurement accuracy of the pipeline geographical position information. Therefore, a filtering method capable of processing the thick tail measurement noise is needed to solve the problems of slipping or jumping of the mileage wheel and the like, and further accurate measurement of the geographical position information of the pipeline is achieved.
There are 5 main articles related to the inertia/mileage wheel pipeline combination positioning technology in CNKI, which are:
the pipeline defect positioning technology based on the volume Kalman smoothing filtering is mainly used for researching that an MEMS strapdown inertial measurement system and a mile wheel form a pipeline defect positioning system, wherein a used filtering algorithm is a volume Kalman filter, and a used filtering algorithm in the invention is a thick tail robust filter, so the method is inconsistent with the used filtering algorithm in the invention.
The feasibility research of the detection and positioning scheme in the small-caliber pipeline adopting MEMS inertial navigation mainly researches a pipeline combined positioning technology based on an MEMS strapdown inertial measurement system, a pipeline odometer, a ground marker and pipeline motion constraint, wherein the used filtering algorithm is an extended Kalman filter, and is inconsistent with a combined device and the filtering algorithm used in the invention.
The application of the integrated navigation technology in the oil and gas pipeline surveying and mapping system mainly researches and utilizes a fiber-optic gyroscope strapdown inertial navigation system, a mileage recorder and a fixed-distance magnetic scale signal to form the long-distance oil and gas pipeline surveying and mapping system, wherein the used filtering algorithm is an L-D improved Kalman filter, and is inconsistent with a combined device and the filtering algorithm used in the invention.
The invention relates to a pipeline central line measuring method based on inertial navigation, which mainly researches a pipeline central line measuring system consisting of a laser gyro strapdown inertial navigation system, a mileage meter and a GPS (global position system).
A high-precision positioning method for pipeline detection based on reverse solution mainly researches a pipeline positioning method based on a strapdown inertial navigation system, a speedometer and position mark points, wherein a filter algorithm used by both forward solution and reverse solution is a Kalman filter and is inconsistent with the filter algorithm used by the invention.
Disclosure of Invention
Aiming at the prior art, the technical problem to be solved by the invention is to provide a pipeline geographical position information measuring method based on thick tail robust filtering, which can filter position measuring wild values when non-Gaussian thick tail measuring noise is caused by the slippage of a mileage wheel, sliding fault or damage of a pipeline motion constraint condition, so as to effectively improve the accuracy and stability of the pipeline geographical position information measurement.
In order to solve the technical problem, the invention provides a pipeline geographical position information measuring method based on thick tail robust filtering, which comprises the following steps:
step 1: fixedly mounting a micro-inertia strapdown measuring system and a mileage wheel on a pipeline geographical position information measuring instrument, and placing the pipeline geographical position information measuring instrument at an inlet of a measured pipeline;
step 2: manually binding the position information of the inlet of the pipeline to be measured to a navigation computer of a micro-inertia strapdown measurement system, wherein the initial position information comprises an initial latitude
Figure BDA0002367362940000021
Initial longitude λ 0 And an initial height h 0 ；
And step 3: preheating and initially aligning the micro-inertia strapdown measurement system;
and 4, step 4: starting a pipeline geographic position information measuring instrument, and driving the instrument to run in a pipeline by using a power device on the measuring instrument so as to acquire sensor data related to the pipeline trend, wherein the sensor data comprises a gyroscope angular speed output
Figure BDA0002367362940000022
Specific force output f of accelerometer b And thereinOutputting delta S by mileage increment of the travel wheel;
and 5: strapdown inertial calculation is carried out by utilizing real-time output data of a gyroscope and an accelerometer to obtain a strapdown attitude matrix
Figure BDA0002367362940000031
East, north and sky speed along a geographic coordinate system
Figure BDA0002367362940000032
And location information
Figure BDA0002367362940000033
The position information comprises latitude
Figure BDA0002367362940000034
Longitude (G)
Figure BDA0002367362940000035
And height
Figure BDA0002367362940000036
And 6: utilizing the strapdown attitude matrix obtained in the step 5 based on the motion constraint conditions of the pipeline
Figure BDA0002367362940000037
Converting the mileage increment information Δ S of the mileage wheel to a geographic coordinate system, i.e.
Figure BDA0002367362940000038
And 7: carrying out dead reckoning by using the mileage increment information of the geographic coordinate system obtained in the step 6 to obtain dead reckoning position information
Figure BDA0002367362940000039
The dead reckoning position information comprises latitude
Figure BDA00023673629400000310
Longitude (longitude)
Figure BDA00023673629400000311
And height
Figure BDA00023673629400000312
And 8: solving the strapdown inertial calculation position information obtained in the step 5
Figure BDA00023673629400000313
And
Figure BDA00023673629400000314
and the dead reckoning position information obtained in the step 7
Figure BDA00023673629400000315
And
Figure BDA00023673629400000316
differencing to obtain system measurement information Z, i.e.
Figure BDA00023673629400000317
And step 9: establishing a state equation and a measurement equation of a pipeline geographic position information measurement system;
step 10: starting a thick tail robust filter, and estimating speed errors delta V of the micro-inertia strapdown measurement system along the east direction, the north direction and the sky direction of a geographic coordinate system E ,δV N ,δV U And position error
Figure BDA00023673629400000325
δλ SINS ,δh SINS ；
Step 11: utilizing the velocity error delta V of the micro inertia strapdown measuring system obtained by estimation in the step 10 along the east direction, the north direction and the sky direction of the geographic coordinate system E ,δV N ,δV U Feeding back to the navigation computer of the micro inertial strapdown measurement system and correcting the measurements made by the micro inertial strapdown measurement systemEast, north and sky speed along a geographic coordinate system
Figure BDA00023673629400000318
Namely, it is
Figure BDA00023673629400000319
Using the micro-inertia strapdown measurement system position error estimated in step 10
Figure BDA00023673629400000320
δλ SINS And δ h SINS The latitude of the calculation position information of the micro inertia strapdown measuring system is corrected by feeding back the navigation computer of the micro inertia strapdown measuring system
Figure BDA00023673629400000321
Longitude (G)
Figure BDA00023673629400000322
And height
Figure BDA00023673629400000323
Namely, it is
Figure BDA00023673629400000324
Corrected position
Figure BDA0002367362940000041
λ SINS And h SINS And outputting the information as the pipeline geographic position information.
The invention also includes:
1. the establishment of the state equation of the pipeline geographical position information measurement system in the step 9 specifically comprises the following steps:
Figure BDA0002367362940000042
the state variable of the system is
Figure BDA0002367362940000043
Wherein:
φ＝[φ E φ N φ U ] T measuring the attitude angle error of the system for micro-inertia strapdown;
δV n ＝[δV E δV N δV U ] T measuring the system speed error for the micro-inertia strapdown;
Figure BDA0002367362940000048
measuring a system position error for the micro-inertial strapdown;
Figure BDA0002367362940000044
a mileage wheel dead reckoning position error;
ε b ＝[ε x ε y ε z ] T the carrier system is the drift of an x, y and z triaxial gyroscope;
Figure BDA0002367362940000045
the carrier system is the zero offset of the x, y and z triaxial accelerometer;
κ D ＝[α θ δK α ψ ] T is a milewheel error, where α θ For pitch setting of declination angle, alpha ψ Setting a deflection angle for the azimuth, wherein delta K is a scale coefficient error;
f is a system state transfer array, gamma is a system noise driving array, W is system noise, and the specific form is as follows:
Figure BDA0002367362940000046
Figure BDA0002367362940000047
Figure BDA0002367362940000051
Figure BDA0002367362940000052
Figure BDA0002367362940000053
Figure BDA0002367362940000054
Figure BDA0002367362940000055
Figure BDA0002367362940000056
Figure BDA0002367362940000061
wherein v is DR The heading speed measured by the mileage wheel can be obtained by the mileage increment measured by the mileage wheel and the time t, namely
Figure BDA0002367362940000062
Figure BDA0002367362940000063
For the projection of the odometer wheel speed in the geographical coordinate system, the strapdown attitude matrix obtained in step 5 may be utilized
Figure BDA0002367362940000064
The stem-coupled speed v measured by the mileage wheel DR Projection to a geographic coordinate system:
Figure BDA0002367362940000065
f E ,f N ,f U for the accelerometer specific force output projection in the geographic coordinate system, the strapdown attitude matrix obtained in step 5 may be utilized
Figure BDA0002367362940000066
Outputting the specific force of the accelerometer obtained in the step 4
Figure BDA0002367362940000067
Projected to a geographical coordinate system
Figure BDA0002367362940000068
Besides, ω is ie The rotational angular velocity of the earth; 0 m×n Is an m multiplied by n order zero matrix; c ij For the strapdown attitude matrix obtained in step 5
Figure BDA0002367362940000069
Ith row and j column elements; r Mh ,R Nh Measuring the main curvature radius of the meridian and the prime unit circle calculated for the geographic position by using a micro-inertia strapdown measurement system; r MhD ,R NhD The radius of curvature of the prime circle and prime circle calculated by using the dead reckoning geographic position.
The establishment of the measurement equation of the pipeline geographical position information measurement system in the step 9 specifically comprises the following steps:
Z＝HX+V
the measurement information Z of the system is obtained in step 8, V is the measurement noise, and H is the measurement matrix
Figure BDA00023673629400000610
2. The design of the thick tail robust filter in step 10 is as follows:
firstly, discretizing the state equation and the measurement equation of the pipeline geographical position information measurement system obtained in the step 9 respectively to obtain:
X k ＝F k-1 X k-1 +Γ k-1 W k-1
Z k ＝H k X k +V k
wherein, F k-1 ,H k ,Γ k-1 The discretized system state transition array, the discretized measurement array and the discretized system noise driving array are adopted; system noise W k-1 And measuring the noise V k Student's t thick tail noise, both with a degree of freedom parameter of γ, i.e.
P(W k )＝St(0,Q k ,γ)
P(V k )＝St(0,R k ,γ)
Wherein Q is k ,R k Respectively a system noise variance matrix and a measured noise variance matrix;
then, setting initial values of filter parameters
Figure BDA0002367362940000071
∑ 0 ,η 0 Thereby initializing the filter;
next, the filter starts to work and starts iterative computation, wherein the k filtering iterative computation step is as follows:
s10.1: update degree of freedom parameter eta' k-1 And calculating a degree of freedom update factor c by using a moment matching method:
Figure BDA0002367362940000072
s10.2: scaling matrix adjustment using degree of freedom update factor c
Figure BDA0002367362940000073
Figure BDA0002367362940000074
S10.3, updating time and calculating the predicted value of the state variable
Figure BDA0002367362940000075
And scale matrix prediction:
Figure BDA0002367362940000076
Figure BDA0002367362940000077
s10.4: updating the measurement, and calculating the state variable estimation value
Figure BDA0002367362940000078
And scale matrix estimation
Figure BDA0002367362940000079
Figure BDA00023673629400000710
Figure BDA00023673629400000711
Wherein n is dz Measuring dimension for quantity, i.e. n dz ＝3；
S10.5: updating the parameter η of degree of freedom k ：
η k ＝η k-1 +n dz
S10.6: output state variable estimation
Figure BDA00023673629400000712
And scale matrix estimation
Figure BDA00023673629400000713
The invention has the beneficial effects that:
the invention provides a combined positioning system formed by a micro inertial strapdown measurement system (MSINS) and a low-cost mileage wheel, and a technology for measuring geographical position information of a pipeline. Specifically, the MSINS and the mileage wheel are used to form an inertia/mileage wheel combination positioning system to provide the geographical location information for the pipeline. When the position measurement outlier information appears due to the fact that the mileage wheel slips or the pipeline motion constraint condition is damaged, the position measurement outlier information is filtered by the thick tail robust filter, and therefore the system provides continuous and high-precision pipeline geographic position information.
Compared with the prior art, the method has the following advantages: and the low-cost micro-inertia strapdown measurement system and the odometer are combined to measure the geographical position information of the pipeline. Meanwhile, the odometer wheel position measurement information noise is modeled as Student's t thick tail noise instead of traditional white gaussian noise. In the process of measuring the geographical position information of the pipeline, when position measurement outlier information occurs due to the fact that a mile wheel slips, a sliding fault and a pipeline motion constraint condition fails, a thick-tail robust filter is used for estimating strapdown inertial resolving errors, meanwhile, the position measurement outlier information can be effectively filtered, the problems that a traditional Kalman filtering algorithm is poor in robustness and unstable in an inertial/mile wheel combined system are solved, and therefore continuous and high-precision geographical position information of the pipeline can be provided.
The beneficial effects of the invention are further illustrated by the following steps: comparing simulation results of the micro inertia strapdown measurement system/odometer combined pipeline geographical position information measurement method based on the thick tail robust filtering (STKF) and the combined positioning method based on the conventional Kalman Filtering (KF).
Drawings
FIG. 1 is a flow chart of a micro inertial strapdown measurement system/odometer wheel combination pipeline geographical location information measurement system work based on thick tail robust filtering;
FIG. 2 is a schematic diagram of a movement track of a pipeline geographical position information measuring system;
FIG. 3 is a comparison of position errors after combined inertial/odometer positioning based on conventional Kalman filtering and based on thick-tailed robust filtering;
FIG. 4 is the results of 20 simulation experiments RMSE;
Detailed Description
The following further describes the embodiments of the present invention with reference to the drawings.
The system power device drives the system power device to operate in the pipeline to acquire sensor data related to the pipeline trend, and strapdown inertial resolution and dead reckoning are respectively carried out; and the difference value between the strapdown inertial calculation position and the dead reckoning position is used as measurement information, position measurement outlier information caused by the slip of a mileage wheel, the sliding fault and the failure of a pipeline motion constraint condition is filtered by a thick tail robust filter, and meanwhile, a strapdown inertial calculation error is estimated and the geographic position information of a pipeline is corrected and output.
The invention is described in more detail below by way of example with reference to fig. 1. A pipeline geographical position information measuring method based on thick tail robust filtering comprises the following specific implementation steps:
step 1, fixedly installing a micro-inertia strapdown measuring system and a mileage wheel on a pipeline geographical position information measuring instrument, and placing the pipeline geographical position information measuring instrument at an inlet of a measured pipeline;
step 2, manually binding the position information of the inlet of the pipeline to be measured to a navigation computer of the micro-inertia strapdown measurement system, wherein the initial position information comprises an initial latitude
Figure BDA0002367362940000091
Initial longitude λ 0 And an initial height h 0 ；
Step 3, preheating and initial alignment are carried out on the micro-inertia strapdown measurement system;
and 4, starting the pipeline geographic position information measuring instrument, and driving the measuring instrument to run in the pipeline by using a power device on the measuring instrument so as to acquire information related to the pipeline trendThe sensor data including a gyroscope angular velocity output
Figure BDA0002367362940000092
Specific force output f of accelerometer b And outputting the mileage increment Delta S of the mileage wheel;
step 5, performing strapdown inertial calculation by utilizing real-time output data of the gyroscope and the accelerometer to obtain a strapdown attitude matrix
Figure BDA0002367362940000093
East, north and sky speed along a geographic coordinate system
Figure BDA0002367362940000094
And location information
Figure BDA0002367362940000095
The position information comprises latitude
Figure BDA0002367362940000096
Longitude (G)
Figure BDA0002367362940000097
And height
Figure BDA0002367362940000098
Step 6, based on the constraint conditions of the pipeline motion, utilizing the strapdown attitude matrix obtained in the step 5
Figure BDA0002367362940000099
Converting the mileage increment information Δ S of the mileage wheel to a geographical coordinate system, i.e.
Figure BDA00023673629400000910
Step 7, carrying out dead reckoning by using the geographical coordinate system mileage increment information obtained in the step 6 to obtain dead reckoning position information
Figure BDA00023673629400000911
The dead reckoning position information comprises latitude
Figure BDA00023673629400000912
Longitude (longitude)
Figure BDA00023673629400000913
And height
Figure BDA00023673629400000914
Step 8, solving the strapdown inertia obtained in the step 5 into position information
Figure BDA00023673629400000915
And
Figure BDA00023673629400000916
and the dead reckoning position information obtained in the step 7
Figure BDA00023673629400000917
And
Figure BDA00023673629400000918
differencing to obtain system measurement information Z, i.e.
Figure BDA00023673629400000919
Step 9, establishing a state equation and a measurement equation of the pipeline geographical position information measurement system;
step 10, starting a thick tail robust filter, and estimating speed errors delta V of the micro inertia strapdown measurement system along east, north and sky directions of a geographic coordinate system E ,δV N ,δV U And position error
Figure BDA00023673629400000920
Step 11, utilizing the micro inertia strapdown measurement system estimated in the step 10Velocity error delta V of system along east, north and sky directions of geographic coordinate system E ,δV N ,δV U Feeding back to the navigation computer of the micro inertial strapdown measurement system and correcting the speed of the micro inertial strapdown measurement system measured along the east, north and sky directions of the geographic coordinate system
Figure BDA00023673629400000921
Namely, it is
Figure BDA00023673629400000922
Using the micro inertial strapdown measurement system position error estimated in step 10
Figure BDA00023673629400000923
δλ SINS And δ h SINS Feeding back to the navigation computer of the micro-inertia strapdown measurement system and correcting the calculated position information latitude of the micro-inertia strapdown measurement system
Figure BDA00023673629400000924
Longitude (G)
Figure BDA0002367362940000101
And height
Figure BDA0002367362940000102
Namely, it is
Figure BDA0002367362940000103
Corrected position
Figure BDA0002367362940000104
λ SINS And h SINS And outputting the information as the pipeline geographic position information.
The invention also includes:
(1) The system state equation in step 9 is established as follows:
Figure BDA0002367362940000105
the state variable of the system is
Figure BDA0002367362940000106
Wherein:
φ＝[φ E φ N φ U ] T -measuring the system attitude angle error for a micro inertial strapdown;
δV n ＝[δV E δV N δV U ] T -measuring the system velocity error for a micro inertial strapdown;
Figure BDA0002367362940000107
-measuring the system position error for micro inertial strapdown;
Figure BDA0002367362940000108
-dead reckoning the position error for the mileage wheel;
ε b ＝[ε x ε y ε z ] T -shifting for a carrier system x, y, z triaxial gyro;
Figure BDA0002367362940000109
-zero offset for the carrier system x, y, z triaxial accelerometer;
κ D ＝[α θ δK α ψ ] T -as odometer wheel error, where α θ For pitch mounting of declination angle, alpha ψ Setting a deflection angle for the azimuth, wherein delta K is a scale coefficient error;
f is a system state transfer array, gamma is a system noise driving array, W is system noise, and the specific form is as follows:
Figure BDA00023673629400001010
Figure BDA0002367362940000111
Figure BDA0002367362940000112
Figure BDA0002367362940000113
Figure BDA0002367362940000114
Figure BDA0002367362940000115
Figure BDA0002367362940000116
Figure BDA0002367362940000121
Figure BDA0002367362940000122
wherein v is DR The heading speed measured by the mileage wheel can be obtained by the mileage increment measured by the mileage wheel and the time t, namely
Figure BDA0002367362940000123
Figure BDA0002367362940000124
For the projection of the odometer wheel speed in the geographical coordinate system, the strapdown attitude matrix obtained in step 5 may be utilized
Figure BDA0002367362940000125
The stem-coupled speed v measured by the mileage wheel DR Projected to a geographic coordinate system
Figure BDA0002367362940000126
f E ,f N ,f U For the projection of the accelerometer specific force output on the geographic coordinate system, the strapdown attitude matrix obtained in step 5 may be utilized
Figure BDA0002367362940000127
Outputting the specific force of the accelerometer obtained in the step 4
Figure BDA0002367362940000128
Projected to a geographical coordinate system
Figure BDA0002367362940000129
In addition to this, ω ie The rotational angular velocity of the earth; 0 m×n Is an m multiplied by n order zero matrix; c ij For the strapdown attitude matrix obtained in step 5
Figure BDA00023673629400001210
Ith row and j column elements; r Mh ,R Nh Measuring the main curvature radius of the meridian and the prime unit circle calculated for the geographic position by using a micro-inertia strapdown measurement system; r is MhD ,R NhD The radius of curvature of the prime circle and prime circle calculated by using the dead reckoning geographic position.
(2) The measurement equation in step 9 is established as follows:
Z＝HX+V
the measurement information Z of the system is obtained in step 8, V is the measurement noise, and H is the measurement matrix
Figure BDA00023673629400001211
(3) The thick tail robust filter in step 10 is designed as follows:
firstly, discretizing the state equation and the measurement equation of the pipeline geographical position information measurement system obtained in the step 9 respectively to obtain
X k ＝F k-1 X k-1 +Γ k-1 W k-1
Z k ＝H k X k +V k
Wherein, F k-1 ,H k ,Γ k-1 The discretized system state transition array, the discretized measurement array and the discretized system noise driving array are adopted; system noise W k-1 And measuring the noise V k Student's t thick tail noise, both with a degree of freedom parameter of γ, i.e.
P(W k )＝St(0,Q k ,γ)
P(V k )＝St(0,R k ,γ)
Wherein Q is k ,R k Respectively, a system noise variance matrix and a measured noise variance matrix.
Then, setting initial values of filter parameters
Figure BDA0002367362940000131
∑ 0 ,η 0 Thereby initializing the filter.
Next, the filter start-up operation starts iterative computation. Wherein, the k filtering iterative computation step is as follows:
(1) updating a degree of freedom parameter eta' k-1 And a degree of freedom update factor c is calculated by using a moment matching method.
Figure BDA0002367362940000132
(2) Scaling matrix adjustment using degree of freedom update factor c
Figure BDA0002367362940000133
Figure BDA0002367362940000134
(3) Updating time and calculating the predicted value of the state variable
Figure BDA0002367362940000135
And a scale matrix predictor.
Figure BDA0002367362940000136
Figure BDA0002367362940000137
(4) Performing measurement update to calculate state variable estimation value
Figure BDA0002367362940000138
And scale matrix estimation
Figure BDA0002367362940000139
Figure BDA00023673629400001310
Figure BDA00023673629400001311
Wherein n is dz Measuring the dimension number, i.e. n dz ＝3。
(5) Updating the degree of freedom parameter eta k 。
η k ＝η k-1 +n dz
(6) Output state variable estimation
Figure BDA0002367362940000141
And scale matrix estimation
Figure BDA0002367362940000142
Details not described in the present specification are well within the skill of those in the art.
Simulation verification:
(1) The main sensor parameters in the micro-inertia strapdown measurement system are as follows:
zero bias stability of the MEMS gyroscope: 1 degree/h;
zero offset stability of the MEMS accelerometer: 10 -4 g (g is gravitational acceleration);
error parameters of the mileage wheel device: the pitching installation declination angle is 0.5 degrees, the azimuth installation declination angle is 0.7 degrees, and the scale coefficient error is 0.002;
(2) In order to simulate the position measurement wild value caused by the slippage of the mileage wheel, the sliding fault and the failure of the pipeline motion constraint condition, the measurement noise V is set as follows:
Figure BDA0002367362940000143
wherein w.p. represents that noise appears with a certain probability, 0.10 represents the probability of appearance of the position measurement field value, and the measurement noise variance matrix R = (diag [10m/Re 10 m)]) 2 And Re is the earth radius.
(3) In the thick-tail robust filter, the filter parameters are set as follows:
degree of freedom eta 0 =5, scale matrix Σ 0 = R, number of iterations N =4.
(4) And (5) carrying out 20 simulation tests, wherein the time length of each simulation test is 1000 seconds. After the initial alignment is completed, the pipeline geographic position information measuring system is set to respectively perform the following movements: firstly, accelerating for 10s along the north direction and then running at a constant speed for 290s; then, the turning (50 s) runs for 100s at a constant speed along the course direction of 90 degrees; is connected withThen, turning again (50 s) and running at constant speed for 490s along the course direction of 180 degrees; finally, the speed is reduced to zero. The acceleration in the operation process is 0.1m/s respectively 2 、-0.1m/s 2 The schematic diagram of the movement track of the pipeline geographical position information measuring system is shown in fig. 2. Evaluating the measurement accuracy of the pipeline geographical position information by using the performance indexes shown in the formulas (2), (3) and (4):
Figure BDA0002367362940000144
Figure BDA0002367362940000145
Figure BDA0002367362940000146
wherein p is k For filtering the corrected position information, mu k For the real position information, M represents the number of simulation steps, and the superscript T represents the matrix transposition.
The invention utilizes the micro inertia strapdown measurement system/odometer combined pipeline geographical position information measurement method based on the thick tail robust filtering (STKF) and the combined positioning method based on the conventional Kalman Filtering (KF) to carry out simulation comparison. The simulation result of the northeast position error corrected by the graph in fig. 3 shows that: the inertia/mileage wheel combination positioning precision based on the conventional Kalman filtering is obviously lower than that of the micro inertia strapdown measurement system/mileage wheel combination pipeline geographical position information measurement method based on the thick tail robust filtering (STKF) provided by the invention. Through 20 times of simulation test results as shown in fig. 4 and table 1, in a 1-kilometer pipeline measurement simulation test, the average measurement error of the pipeline geographical position information provided by the invention is 1.67 meters, and the measurement precision is improved by 49.08% compared with that of the conventional method, so that the precision requirement of the urban underground pipeline geographical position information measurement can be met.
TABLE 1 EMAX and ARMSE results of 120 simulation tests
Figure BDA0002367362940000151
The invention relates to a pipeline geographical position information measuring method based on a thick tail robust filtering micro-inertia strapdown measuring system/mile wheel combination. The output position of the mileage wheel is used as measurement information to assist a micro-inertia strapdown measurement system, and strapdown inertia calculation errors are estimated and corrected through a thick tail robust filter, so that continuous and high-precision pipeline geographical position information is provided. Meanwhile, when a thick tail robust filter is designed, measurement noise is modeled into Student's t thick tail noise distribution, so that a position measurement wild value can be filtered when the position measurement noise is not Gaussian thick tail noise caused by the fact that a mileage wheel slips, a sliding fault or a pipeline motion constraint condition is damaged, and the accuracy and the stability of pipeline geographic position information measurement are effectively improved.

Claims (3)

1. A pipeline geographical position information measuring method based on thick tail robust filtering is characterized by comprising the following steps:
step 1: fixedly mounting a micro-inertia strapdown measuring system and a mileage wheel on a pipeline geographical position information measuring instrument, and placing the pipeline geographical position information measuring instrument at an inlet of a measured pipeline;
step 2: manually binding the position information of the inlet of the pipeline to be measured to a navigation computer of a micro-inertia strapdown measurement system, wherein the initial position information comprises an initial latitude
Figure FDA00023673629300000120
Initial longitude λ 0 And an initial height h 0 ；
And step 3: preheating and initially aligning the micro-inertia strapdown measurement system;
and 4, step 4: starting a pipeline geographic position information measuring instrument, and driving the instrument to run in a pipeline by using a power device on the measuring instrument so as to acquire sensor data related to the pipeline trend, wherein the sensor data comprises a gyroscope angular speed output
Figure FDA0002367362930000011
Specific force output f of accelerometer b And mileage wheel mileage increment output Δ S;
and 5: strapdown inertial calculation is carried out by utilizing real-time output data of a gyroscope and an accelerometer to obtain a strapdown attitude matrix
Figure FDA0002367362930000012
East, north and sky speed along a geographic coordinate system
Figure FDA0002367362930000013
And location information
Figure FDA0002367362930000014
The position information comprises latitude
Figure FDA0002367362930000015
Longitude (G)
Figure FDA0002367362930000016
And height
Figure FDA0002367362930000017
Step 6: utilizing the strapdown attitude matrix obtained in the step 5 based on the constraint condition of the pipeline motion
Figure FDA0002367362930000018
Converting the mileage increment information Δ S of the mileage wheel to a geographical coordinate system, i.e.
Figure FDA0002367362930000019
And 7: carrying out dead reckoning by using the mileage increment information of the geographic coordinate system obtained in the step 6 to obtain dead reckoning position information
Figure FDA00023673629300000110
The dead reckoning position information comprises latitude
Figure FDA00023673629300000111
Longitude (G)
Figure FDA00023673629300000112
And height
Figure FDA00023673629300000113
And 8: solving the strapdown inertial calculation position information obtained in the step 5
Figure FDA00023673629300000114
And
Figure FDA00023673629300000115
and the dead reckoning position information obtained in the step 7
Figure FDA00023673629300000116
And
Figure FDA00023673629300000117
differencing to obtain system measurement information Z, i.e.
Figure FDA00023673629300000118
And step 9: establishing a state equation and a measurement equation of a pipeline geographic position information measurement system;
step 10: starting a thick tail robust filter, and estimating speed errors delta V of the micro-inertia strapdown measurement system along the east direction, the north direction and the sky direction of a geographic coordinate system E ,δV N ,δV U And position error
Figure FDA00023673629300000121
δλ SINS ,δh SINS ；
Step 11: utilizing the velocity error delta V of the micro inertia strapdown measuring system obtained by estimation in the step 10 along the east direction, the north direction and the sky direction of the geographic coordinate system E ,δV N ,δV U Feeding back to the navigation computer of the micro inertial strapdown measurement system and correcting the speed of the micro inertial strapdown measurement system measured along the east, north and sky directions of the geographic coordinate system
Figure FDA00023673629300000119
Namely, it is
Figure FDA0002367362930000021
Using the micro inertial strapdown measurement system position error estimated in step 10
Figure FDA0002367362930000029
δλ SINS And δ h SINS The latitude of the calculation position information of the micro inertia strapdown measuring system is corrected by feeding back the navigation computer of the micro inertia strapdown measuring system
Figure FDA0002367362930000022
Longitude (G)
Figure FDA0002367362930000023
And height
Figure FDA0002367362930000024
Namely, it is
Figure FDA0002367362930000025
Corrected position
Figure FDA00023673629300000210
λ SINS And h SINS And outputting the information as the pipeline geographic position information.
2. The pipeline geographical position information measuring method based on the thick tail robust filtering as claimed in claim 1, wherein: step 9, establishing a state equation of the pipeline geographical position information measurement system specifically comprises:
Figure FDA0002367362930000026
the state variable of the system is
Figure FDA0002367362930000027
Wherein:
φ＝[φ E φ N φ U ] T measuring the attitude angle error of the system for micro-inertia strapdown;
δV n ＝[δV E δV N δV U ] T measuring the system speed error for the micro-inertia strapdown;
Figure FDA00023673629300000211
measuring a system position error for the micro-inertial strapdown;
Figure FDA00023673629300000212
a mileage wheel dead reckoning position error;
ε b ＝[ε x ε y ε z ] T the carrier system is the drift of an x, y and z triaxial gyroscope;
Figure FDA0002367362930000028
the carrier system is the zero offset of the x, y and z triaxial accelerometer;
κ D ＝[α θ δK α ψ ] T is a milewheel error, where α θ For pitch setting of declination angle, alpha ψ Mounting a deflection angle for the azimuth, wherein delta K is a scale coefficient error;
f is a system state transfer array, gamma is a system noise driving array, W is system noise, and the specific form is as follows:
Figure FDA0002367362930000031
Figure FDA0002367362930000032
Figure FDA0002367362930000033
Figure FDA0002367362930000034
Figure FDA0002367362930000035
Figure FDA0002367362930000036
Figure FDA0002367362930000041
Figure FDA0002367362930000042
Figure FDA0002367362930000043
wherein v is DR The heading speed measured by the mileage wheel can be obtained by the mileage increment measured by the mileage wheel and the time t, namely
Figure FDA0002367362930000044
Figure FDA0002367362930000045
For the projection of the odometer wheel speed in the geographical coordinate system, the strapdown attitude matrix obtained in step 5 may be utilized
Figure FDA0002367362930000046
The stem-coupled speed v measured by the mileage wheel DR Projection onto a geographic coordinate system:
Figure FDA0002367362930000047
f E ,f N ,f U for the projection of the accelerometer specific force output on the geographic coordinate system, the strapdown attitude matrix obtained in step 5 may be utilized
Figure FDA0002367362930000048
Outputting the specific force of the accelerometer obtained in the step 4
Figure FDA0002367362930000049
Projected to a geographical coordinate system
Figure FDA00023673629300000410
Besides, ω is ie The rotational angular velocity of the earth; 0 m×n Is an m multiplied by n order zero matrix; c ij For the strapdown attitude matrix obtained in step 5
Figure FDA00023673629300000411
Row i and column j; r Mh ,R Nh Measuring the main curvature radius of the meridian and the prime unit circle calculated for the geographic position by using a micro-inertia strapdown measurement system; r MhD ,R NhD Calculating the main curvature radius of a meridian circle and a prime circle by using the dead reckoning geographic position;
step 9, the establishment of the measurement equation of the pipeline geographical location information measurement system specifically comprises:
Z＝HX+V
the measurement information Z of the system is obtained in step 8, V is the measurement noise, and H is the measurement matrix
Figure FDA0002367362930000051
。
3. The pipeline geographical position information measurement method based on the thick tail robust filtering as claimed in claim 1 or 2, wherein: step 10, the design of the thick tail robust filter is as follows:
firstly, discretizing the state equation and the measurement equation of the pipeline geographical position information measurement system obtained in the step 9 respectively to obtain:
X k ＝F k-1 X k-1 +Γ k-1 W k-1
Z k ＝H k X k +V k
wherein, F k-1 ,H k ,Γ k-1 The discretized system state transition array, the discretized measurement array and the discretized system noise driving array are obtained; system noise W k-1 And measuring the noise V k Student's t thick tail noise, both with a degree of freedom parameter of γ, i.e.
P(W k )＝St(0,Q k ,γ)
P(V k )＝St(0,R k ,γ)
Wherein，Q k ,R k Respectively a system noise variance matrix and a measured noise variance matrix;
then, setting initial values of filter parameters
Figure FDA0002367362930000052
∑ 0 ,η 0 Thereby initializing the filter;
next, the filter starts to work and starts iterative computation, wherein the k filtering iterative computation step is as follows:
s10.1: updating a degree of freedom parameter eta' k-1 And calculating a degree of freedom update factor c by using a moment matching method:
Figure FDA0002367362930000053
s10.2: scaling matrix adjustment using degree of freedom update factor c
Figure FDA0002367362930000054
Figure FDA0002367362930000055
S10.3, updating time and calculating the predicted value of the state variable
Figure FDA0002367362930000056
And scale matrix prediction:
Figure FDA0002367362930000057
Figure FDA0002367362930000058
s10.4: updating the measurement, and calculating the state variable estimation value
Figure FDA0002367362930000059
And scale matrix estimation
Figure FDA00023673629300000510
Figure FDA0002367362930000061
Figure FDA0002367362930000062
Wherein n is dz Measuring the dimension number, i.e. n dz ＝3；
S10.5: updating the degree of freedom parameter eta k ：
η k ＝η k-1 +n dz
S10.6: output state variable estimation
Figure FDA0002367362930000063
And scale matrix estimation
Figure FDA0002367362930000064
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CN111912425A (en) * 2020-08-09 2020-11-10 长沙智来测控科技有限公司 Pipeline measurement system and method
CN112083465A (en) * 2020-09-18 2020-12-15 德明通讯（上海）有限责任公司 Position information acquisition system and method
CN112508971B (en) * 2020-12-21 2023-08-22 华南理工大学 Weld joint positioning method, system and storage medium based on simulation structure light stripe
CN114383610B (en) * 2021-12-24 2024-07-16 郑州恒达智控科技股份有限公司 Jitter detection segmentation filtering method based on mobile three-dimensional scanning technology
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CN114608570B (en) * 2022-02-25 2023-06-30 电子科技大学 Multi-mode self-switching pipeline instrument self-adaptive precise positioning method
CN114909608B (en) * 2022-05-27 2023-09-19 哈尔滨工程大学 Non-excavation pipeline positioning method based on MIMU/mileage wheel/photoelectric speed measurement module combination
CN117951653B (en) * 2024-01-31 2024-07-26 兰州理工大学 Smooth tracking method based on Student's t process regression

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101413799A (en) * 2008-11-26 2009-04-22 大连理工大学 Combined navigation system for outdoor movable target
CN109131341A (en) * 2018-07-09 2019-01-04 中国北方车辆研究所 It is a kind of for taking turns the driving wheel slip detecting method and system of independent drive vehicles entirely

Family Cites Families (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1729145B1 (en) * 2005-06-02 2013-08-07 GMV Aerospace and Defence S.A. Method and system for providing GNSS navigation position solution with guaranteed integrity in non-controlled environments
US10403007B2 (en) * 2017-03-07 2019-09-03 Children's Medical Center Corporation Registration-based motion tracking for motion-robust imaging
CN109061579A (en) * 2018-08-03 2018-12-21 中国航空工业集团公司雷华电子技术研究所 A kind of robust volume filtering method of band thickness tail noise
CN109459019B (en) * 2018-12-21 2021-09-10 哈尔滨工程大学 Vehicle navigation calculation method based on cascade adaptive robust federal filtering
CN109724599B (en) * 2019-03-12 2023-08-01 哈尔滨工程大学 Wild value resistant robust Kalman filtering SINS/DVL integrated navigation method
CN109974697B (en) * 2019-03-21 2022-07-26 中国船舶重工集团公司第七0七研究所 High-precision mapping method based on inertial system

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101413799A (en) * 2008-11-26 2009-04-22 大连理工大学 Combined navigation system for outdoor movable target
CN109131341A (en) * 2018-07-09 2019-01-04 中国北方车辆研究所 It is a kind of for taking turns the driving wheel slip detecting method and system of independent drive vehicles entirely

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