CN106126834B - A kind of best linear determining method of the orbit plane based on inertial navigation angle measurement - Google Patents
A kind of best linear determining method of the orbit plane based on inertial navigation angle measurement Download PDFInfo
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Abstract
The invention discloses a kind of best linear determining methods of orbit plane based on inertial navigation angle measurement, purpose is, meet that railroad track demand of technical standard, result precision are high, treatment process calculation amount is small, data processing time is short, used technical solution are as follows: on the basis of being based on inertial navigation angle measurement, in conjunction with the best wiresizing optimization model of orbit plane, outline segmentation is carried out to track according to fixed length curvature curve least square fitting slope variation first, then carry out accurate segmentation using combined iteration algorithm and is fitted best linear parameter.
Description
Technical field
The invention belongs to the data processing fields in orbit geometry parameter detection, and in particular to one kind is based on inertial navigation angular amount
The best linear determining method of the orbit plane of survey.
Background technique
Rail track is to geometric parameter, such as track is linear and track alignment irregularity etc., with climatic environment and fortune
The change of battalion's load is constantly changing, and has an impact to train operating safety.The track rail difference linear and linear ideal to reality
As track alignment irregularity, track alignment irregularity will cause vehicle pitching, rolling stock wheel increases the horizontal force of rail, seriously
When may cause that widening of gauge, the section of track be traversing or even train derailing.Therefore, reinforce track rail to detect to geometric parameter to guarantee
Traffic safety is one of the emphasis of railway maintenance work.
Orbit parameter detection method widely used at present has inertial reference method, chord measurement and method of absolute coordinate system.Inertia base
Quasi- method be according in car body mass block displacement and its relative displacement calculates track irregularity between axle box method, be chiefly used in big
Type net rail detects vehicle, and the examined speed of precision is affected, and is not suitable for low speed line detection；Chord measurement is chiefly used in rail inspection instrument,
Have the advantages that the not examined speed of measured value influences, but this method " pushing away greatly with small ", all can not really reflect track
State, therefore error is larger；Method of absolute coordinate system cooperates the absolute position of observation point on CPIII control point survey track using total station
Coordinate is set, is then fitted orbit geometry parameter using least-squares algorithm, this method detection speed is slow, needs to establish CPIII control
Making point and carrying out long term maintenance, Data processing also needs Reference Design data, adds somewhat to railway maintenance work
Cost and complexity.
Different from the above traditional detection method using position measurement and position versus as means, researcher proposes a kind of base
In the track detection method of inertia measurement, odometer is cooperated to detect track rail to geometric parameter by measurement direction angle,
This method makes full use of the high precision of gyroscope measurement angle, has high detection efficiency, precision height, testing result not examined
The advantages that rate limitation, is with a wide range of applications.Currently, the track irregularity parameter based on the detection method calculates mostly
Rely on original design data, and for some design datas missing or track is linear need re-optimization whole positive in the case of, then require
The best linear parameter of orbit plane is determined from the orbital direction angle comprising track irregularity and measurement noise, mileage.
Summary of the invention
In order to solve the problems in the prior art, the present invention propose it is a kind of have meet railroad track demand of technical standard,
As a result the orbit plane based on inertial navigation angle measurement for the advantage that precision is high, treatment process calculation amount is small, data processing time is short
Best linear determining method.
In order to achieve the goal above, the technical scheme adopted by the invention is as follows: the following steps are included:
1) inertial navigation angle measurement is carried out to orbit plane and obtains inertial navigation deflection data sequence, by inertial navigation direction angular data sequence
Column obtain the curvature Variation at each test point along route mileage difference, and form orderly song with the mileage at test point
Rate-mileage sequence, to obtain curvature-mileage curve；
2) to two segment data of front and back of the test point i in the curvature of step 1)-mileage curveWithIt is quasi- using least-squares line respectively
Hop algorithm is fitted, miIndicate the mileage at measuring point i, kiIt indicates the curvature at measuring point i, calculates the last period matched curve with after
The slope differences of one section of matched curve are based on least square fitting slope variation according to the linear curvature feature of track and curvature curve
Rule is segmented to obtain multiple groups waypoint coordinate, so that orbit plane is divided into multistage fundamental line tuple to linear；
3) linear according to track linear curvature feature fitting first to the waypoint of each section of fundamental line tuple, then group
It is optimal to the fundamental line tuple to close iteration, next fundamental line tuple is reprocessed, after finally integrating to multistage fundamental line tuple
The best linear parameter of whole track is obtained, so that it is determined that best linear.
Step 1) the mean curvature variation characteristic should be similar to the linear curvature feature of ideal track, and wherein ideal track is linear
Curvature feature is linear for the symmetrical basic model track as made of straight line-easement curve-circular curve-easement curve-Straight Combination,
The inertial navigation deflection of straightway remains unchanged, and straightway curvature is 0；Circular curve segment inertial navigation deflection changes linearly, circular curve
It is circular curve radius that section curvature, which is steady state value K ∝ a 1/R, R,；Easement curve section inertial navigation deflection changes in second-degree parabola, bent
Rate linear change between 0~K with mileage.
Curvature obtained in the step 1)-mileage curve need to carry out abandoning rough error and median filter process.
The slope differences of the case where being positive in the step 2) for circular curve curvature, two sections of matched curves are gentle in point of tangent to spiral
There is minimum at straight point, has maximum at point of spiral to curve and point of curve to spiral；The case where being negative for circular curve curvature, two sections of fittings are bent
The slope differences of line have minimum at point of spiral to curve and point of curve to spiral, have maximum at point of tangent to spiral and point of spiral to tangent.
Being fitted linear step according to the linear curvature feature of track in the step 3) includes: starting point determining first, one group
Waypoint and terminal abscissa (M0,M1,M2,M3,M4,Me), then in conjunction with the feature of the linear curvature of orbit plane, according to following
Principle determines its curvature value:Wherein, straightway curvature is 0, circle
Curved section curvature is proportional to 1/R, MjThe abscissa of measuring point j is represented, the value of ω is that abscissa is M2To M3Measuring point curvature value it is flat
Mean, E (k (M2),k(M2+1),…,k(M3)) represent to k (M2),k(M2+1),…,k(M3) it is a series of number be averaging, finally will
Curvature-mileage curve that each point that coordinate determines is fitted after being gradually connected, the deflection-being fitted after mileage integral
Mileage curve, and calculate the target function value under each waypoint combination.
The specific steps of combined iteration in the step 3) are as follows: determine the region of search range that iteration carries out first, substitute into general
It is initial target solution (dS, X) that slightly waypoint track is linear, calculates initial target functional value f (dS, X) using objective function, described
Objective function are as follows: min (f (dS, X))=∑ Δi 2, dS is independent variable, and S can be obtained by integrating to dS along mileage, and wherein S is for rail
The ordered set of deflection is fitted at each measuring point mileage in road and the mileage, X is the ordered set of metric data mileage, deflection
It closes, Δi=αi-αi' indicate measuring point direction angle alphaiWith fitting direction angle alphai' deviation；
Then change waypoint combination in region of search, redefine the linear (dS of trackn, X), calculating target function value f
(dSn, X), if f (dSn, X) and < f (dS, X), then receive new explanation, otherwise receives former solution；
Finally judge whether all waypoints combination in traversal search domain, be then algorithm termination, otherwise repeatedly step 2).
Constraint condition is introduced in the objective function constitutes the best wiresizing optimization model of orbit plane, constraint condition are as follows:
In formula: kZ=0 indicates that the curvature of straightway is 0, kci=εiThe curvature for indicating i-th section of circular curve is certain value εi,
kh(i-1)=a* εi+b(i-1)Indicate that each measuring point curvature is 0 to ε on the preceding easement curve of i-th section of circular curveiBetween linear change,
kh(i-1)=-a* εi+b(i+1)Indicate that each measuring point curvature is in ε on the rear easement curve of i-th section of circular curveiTo 0 linear change；Respectively smallest curve radius as defined in design specification, smallest circle length of curve and minimum length of transition curve；
lformer,llatterRespectively indicate the length of the two sections of easement curves in same circular curve front and back.
Compared with prior art, track curvature curve of the invention is based on least square fitting slope variation rule, in conjunction with
Symmetrical basic model track curvature changing rule can carry out outline segmentation to track, use group according to previous step outline segmentation result
Close the best linear parameter that iterative algorithm gradually handles multistage fundamental line tuple available whole track after integration.This hair
It is bright that track curvature changing rule is based in linear fitting, therefore meet Railway Design code requirement.The present invention is changed by combination
Optimal trajectory parameter is determined for algorithm, and the region of search traversed is limited, therefore result precision is high, treatment process calculation amount is small, number
According to short processing time.
It further, include measurement error and track irregularity in curvature-mileage curve that metric data obtains, by abandoning
Rough error and median filtering can obtain and the more similar curvature-mileage curve of the linear curvature feature of ideal track.
Detailed description of the invention
Fig. 1 is that the ideal orientation angle that circular curve curvature is the symmetrical basic model railroad track horizontal alignment of timing changes with mileage
Curve graph；
Fig. 2 is that the desired curvature that circular curve curvature is the symmetrical basic model railroad track horizontal alignment of timing changes song with mileage
Line chart；
Fig. 3 is that circular curve curvature is timing track curvature curve least square fitting slope variation rule figure；
Fig. 4 is that the ideal orientation angle of symmetrical basic model railroad track horizontal alignment when circular curve curvature is negative changes song with mileage
Line chart；
Fig. 5 is the desired curvature of symmetrical basic model railroad track horizontal alignment when circular curve curvature is negative with mileage change curve
Figure；
Fig. 6 is track curvature curve least square fitting slope variation rule figure when circular curve curvature is negative；
Fig. 7 is the comparison of the linear and best linear definitive result of the linear measurement of orbit plane, to measure curvature, filtering curvature
And optimization curvature indicates；
Fig. 8 is the comparison of the linear and best linear definitive result of the linear measurement of orbit plane, with measurement direction angle and optimization
Deflection indicates；
Fig. 9 is flow chart of the method for the present invention.
Specific embodiment
Below with reference to specific embodiment and Figure of description the present invention will be further explained explanation.
The present invention specifically includes the following steps:
The first step, data prediction: carrying out inertial navigation angle measurement to orbit plane and obtain inertial navigation deflection data sequence, will
Inertial navigation deflection data sequence obtained in detection process obtains the Curvature varying at each test point: K=d along route mileage difference
α/dm, positive and negative expression circular curve bending direction form orderly curvature-mileage sequence with mileage at the point, it is inner to obtain curvature-
Journey curve.It include measurement error and track irregularity in the curvature that metric data obtains-mileage curve, by abandoning rough error in
Value filtering can obtain curvature-mileage curve more similar with the linear curvature feature of ideal track.
Wherein, the linear curvature feature of the ideal track is directed to straight by straight line-easement curve-circular curve-easement curve-
The symmetrical basic model track that line is composed is linear, and the analysis linear direction corner characteristics along mileage of track have: straightway deflection
It remains unchanged, circular curve segment deflection linear change, easement curve section deflection changes in second-degree parabola, as shown in Figure 1.Its
It is 0 that curvature, which changes with mileage in straightway curvature, and circular curve segment curvature is a steady state value K ∝ 1/R (R is circular curve radius), is delayed
And curved section curvature with mileage the linear change between 0 and K, as shown in Figure 2.
Second step, the outline segmentation based on track curvature curve least square fitting slope variation track: one section of definition is complete
Whole straight line-easement curve-circular curve-easement curve-straight line linear combination is a fundamental line tuple.The song that the first step is obtained
Two segment datas before and after measuring point i in rate-mileage curveWithIt is fitted respectively using least squares line fitting algorithm, miIt indicates at measuring point i
Mileage, kiIt indicates the curvature at measuring point i, the slope differences of the last period matched curve and latter section of matched curve is calculated, according to rail
The linear curvature feature in road and curvature curve are based on least square fitting slope variation rule can be to linear carry out outline segmentation
Multiple groups waypoint coordinate is obtained, track is divided into multistage fundamental line tuple.
Wherein, it is to curvature-mileage curve that the track curvature curve, which is based on least square fitting slope variation rule,
In measuring point i before and after two segment datasWith
It is fitted respectively using least squares line fitting algorithm, calculates the slope of the last period matched curve and latter section of matched curve
Difference, slope differences have extreme value at each waypoint.The case where being positive for circular curve curvature, it is gentle in point of tangent to spiral by taking Fig. 1 as an example
There is minimum at straight point, has maximum at point of spiral to curve and point of curve to spiral, as shown in Figure 3；The case where being negative for circular curve curvature,
There is minimum at point of spiral to curve and point of curve to spiral, has maximum at point of tangent to spiral and point of spiral to tangent.Track turn to it is opposite with Fig. 1 when deflection with
Mileage change curve as shown in figure 4, curvature with mileage change curve as shown in figure 5, track curvature curve at this time is based on minimum
Two to multiply fit slope changing rule as shown in Figure 6.
Third step, the linear optimization algorithm of track based on combined iteration: for the waypoint of each fundamental line tuple, first root
Linear according to the linear curvature feature fitting of ideal track, then combined iteration is optimal to the fundamental line tuple, reprocesses next basic
Line element group, algorithm flow chart are as shown in Figure 9.The linear fitting of track should carry out as follows: determine starting point, a set of segmentation point and terminal
Abscissa (M0,M1,M2,M3,M4,Me) after, it, should be true according to following principle in conjunction with the feature of Fig. 1-2 middle orbit horizontal alignment curvature
Its fixed curvature value:Wherein, straightway curvature is 0, circular curve segment
Curvature is proportional to 1/R, MjThe abscissa of measuring point j is represented, the value of ω is that abscissa is M2To M3Measuring point curvature value average, E
(k(M2),k(M2+1),…,k(M3)) represent to k (M2),k(M2+1),…,k(M3) it is a series of number be averaging, by coordinate determine
Curvature-mileage curve that each point is fitted after being gradually connected, the deflection-mileage curve being fitted after mileage integral,
It is possible thereby to calculate the target function value under each waypoint combination.Use the multistage fundamental line of combined iteration algorithm process whole
Tuple, the best linear parameter of available whole track after integration, wherein optimal curvatures and measuring value compare as shown in fig. 7,
Optimum orientation angle and the comparison of original measuring value are as shown in Figure 8.
Wherein, the combined iteration algorithm is to be used as the waypoint combination in the certain threshold range of outline waypoint to search
Rope domain, all combinations determine the optimal linear algorithms of track in traversal search domain, and steps are as follows: step 1: determining that iteration carries out
Region of search range, substitute into outline waypoint track it is linear be initial target solution (dS, X), calculate initial target functional value f (dS,
X).Step 2: change waypoint combination in region of search, redefine the linear (dS of trackn, X), calculating target function value f
(dSn, X), if f (dSn, X) and < f (dS, X), then receive new explanation, otherwise receives former solution.Step 3: judge whether traversal search domain
Interior all waypoints combination is then algorithm termination, otherwise repeatedly step 2.
Wherein, the objective function are as follows: min (f (dS, X))=∑ Δi 2, wherein dS is independent variable, and meaning is track
The ordered set { (m of regressive curvature value at each measuring point mileage and the mileage1,k1),(m2,k2),…,(mn,kn), to the edge dS
Mileage, which carries out integral, can obtain S, and meaning is that the ordered set of deflection is fitted at each measuring point mileage of track and the mileage
{(m1,α1),(m2,α2),…,(mn,αn), it can differentiate that track is linear by S and dS, calculate track linear parameter (linear length, circle
Sweep etc.), the mileage at linear start, end, therefore available all fronts Track desigh parameter；X be metric data mileage,
Ordered set the X={ (m of deflection1,α1),(m2,α2),…,(mn,αn)}；Use Δi=αi-αi' indicate measuring point deflection and intend
Close the deviation of deflection.Objective function using minimize each measuring point deflection and be fitted deflection sum of square of deviations as target,
The best wiresizing optimization model of orbit plane is constituted together with constraint condition, solution is each for the track for meeting railroad track design specification
Optimum orientation angle sequence at measuring point can calculate the best linear parameter of track by it.
Wherein, the constraint condition should meet the linear curvature variation requirement of track and railroad track design rule
All kinds of parameter minimum values requirement of model defined, and should to meet front and back length of transition curve equal for symmetrical basic alignment.Therefore
Prescribed Properties:
In formula: kZ=0 indicates that the curvature of straightway is 0, kci=εiThe curvature for indicating i-th section of circular curve is certain value εi,
kh(i-1)=a* εi+b(i-1)Indicate that each measuring point curvature is 0 to ε on the preceding easement curve of i-th section of circular curveiBetween linear change,
kh(i-1)=-a* εi+b(i+1)Indicate that each measuring point curvature is in ε on the rear easement curve of i-th section of circular curveiTo 0 linear change；Respectively smallest curve radius as defined in design specification, smallest circle length of curve and minimum length of transition curve；
lformer,llatterRespectively indicate the length of the two sections of easement curves in same circular curve front and back.
Claims (5)
1. a kind of best linear determining method of orbit plane based on inertial navigation angle measurement, which comprises the following steps:
1) inertial navigation angle measurement is carried out to orbit plane and obtains inertial navigation deflection data sequence, by inertial navigation deflection data sequence edge
Route mileage difference obtains the curvature Variation at each test point, and it is inner with the mileage at test point to form orderly curvature-
Program column, to obtain curvature-mileage curve；
2) to two segment data of front and back of the test point i in the curvature of step 1)-mileage curve
WithIt is fitted respectively using least squares line fitting algorithm, miIndicate measuring point i
The mileage at place, kiIt indicates the curvature at measuring point i, calculates the slope differences of the last period matched curve and latter section of matched curve, according to
The linear curvature feature of track and curvature curve are based on least square fitting slope variation rule, to it is linear be segmented to obtain it is more
Set of segmentation point coordinate, so that orbit plane is divided into multistage fundamental line tuple；
3) to the waypoint of each section of fundamental line tuple, linear according to the linear curvature feature fitting of track first, then combination changes
In generation, is optimal to the fundamental line tuple, reprocesses next fundamental line tuple, after finally integrating to multistage fundamental line tuple to obtain the final product
To the best linear parameter of whole track, so that it is determined that best linear；Linear step is fitted according to the linear curvature feature of track
It include: starting point determining first, a set of segmentation point and terminal abscissa (M0,M1,M2,M3,M4,Me), then in conjunction with orbit plane
The feature of linear curvature determines its curvature value according to following principle:
Wherein, straightway curvature is 0, and circular curve segment curvature is proportional to 1/R, MjThe abscissa of measuring point j is represented, the value of ω is that abscissa is
M2To M3Measuring point curvature value average, E (k (M2),k(M2+1),…,k(M3)) represent to k (M2),k(M2+1),…,k(M3)
A series of numbers are averaging, the curvature-mileage curve being fitted after finally each point that coordinate determines gradually is connected, along mileage product
Deflection-mileage the curve being fitted after point, and calculate the target function value under each waypoint combination；
The specific steps of combined iteration are as follows: determine the region of search range that iteration carries out first, it is linear to substitute into outline waypoint track
For initial target solution (dS, X), initial target functional value f (dS, X) is calculated using objective function, the objective function are as follows: min (f
(dS, X))=∑ Δi 2, dS is independent variable, and S can be obtained by integrating to dS along mileage, and wherein S is for each measuring point mileage of track
And the ordered set of deflection is fitted at the mileage, X is the ordered set of metric data mileage, deflection, Δi=αi-αi' table
Show measuring point direction angle alphaiWith fitting direction angle alphai' deviation；
Then change waypoint combination in region of search, redefine the linear (dS of trackn, X), calculating target function value f (dSn,
X), if f (dSn, X) and < f (dS, X), then receive new explanation, otherwise receives former solution；
Finally judge whether all waypoints combination in traversal search domain, be then algorithm termination, otherwise repeatedly step 2).
2. a kind of best linear determining method of orbit plane based on inertial navigation angle measurement according to claim 1, special
Sign is that step 1) the mean curvature variation characteristic should be similar to the linear curvature feature of ideal track, and wherein ideal track is linear
Curvature feature is linear for the symmetrical basic model track as made of straight line-easement curve-circular curve-easement curve-Straight Combination,
The inertial navigation deflection of straightway remains unchanged, and straightway curvature is 0；Circular curve segment inertial navigation deflection changes linearly, circular curve
It is circular curve radius that section curvature, which is steady state value K ∝ a 1/R, R,；Easement curve section inertial navigation deflection changes in second-degree parabola, bent
Rate linear change between 0~K with mileage.
3. a kind of best linear determining method of orbit plane based on inertial navigation angle measurement according to claim 2, special
Sign is that curvature obtained in the step 1)-mileage curve need to carry out abandoning rough error and median filter process.
4. a kind of best linear determining method of orbit plane based on inertial navigation angle measurement according to claim 1, special
The slope differences of the case where sign is, is positive in the step 2) for circular curve curvature, two sections of matched curves are gentle in point of tangent to spiral
There is minimum at straight point, has maximum at point of spiral to curve and point of curve to spiral；The case where being negative for circular curve curvature, two sections of fittings are bent
The slope differences of line have minimum at point of spiral to curve and point of curve to spiral, have maximum at point of tangent to spiral and point of spiral to tangent.
5. a kind of best linear determining method of orbit plane based on inertial navigation angle measurement according to claim 1, special
Sign is, constraint condition is introduced in the objective function and constitutes the best wiresizing optimization model of orbit plane, constraint condition are as follows:
In formula: kZ=0 indicates that the curvature of straightway is 0, kci=εiThe curvature for indicating i-th section of circular curve is certain value εi, kh(i-1)
=a* εi+b(i-1)Indicate that each measuring point curvature is 0 to ε on the preceding easement curve of i-th section of circular curveiBetween linear change, kh(i-1)=-
a*εi+b(i+1)Indicate that each measuring point curvature is in ε on the rear easement curve of i-th section of circular curveiTo 0 linear change；Rmin,lminPoint
It Wei not smallest curve radius, smallest circle length of curve as defined in design specification and minimum length of transition curve；lformer,llatterPoint
The length of the two sections of easement curves in same circular curve front and back is not indicated.
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