CN107193888A - A kind of urban road network model towards track level navigator fix - Google Patents
A kind of urban road network model towards track level navigator fix Download PDFInfo
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- G—PHYSICS
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- 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
- G01C21/26—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for navigation in a road network
- G01C21/28—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for navigation in a road network with correlation of data from several navigational instruments
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- G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
- G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
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Abstract
A kind of urban road network model towards track level navigator fix, the model is main to be made up of road geographic information layer, both sides of the road building information layer and the part of road plane lane line Information Level three.The road plane lane line Information Level in the model uses the plane lane line of three Cardinal Based on Interpolating Spline fit object roads simultaneously, so that linear have preferable slickness, continuity and plasticity, the SPL can preferably adapt to the characteristics of urban road Curvature varying is big, and the parameter of acquisition can more realistically reflect the plane track present situation of urban road.Urban road network model proposed by the invention, extend the attribute of traditional road level numerical map, improve the precision of traditional road level numerical map, have the advantages that information content is complete, precision is high, applicability is wide, under complicated urban traffic environment, realize that vehicle is accurate, continue, real-time navigation is positioned, meeting the demand of track level navigator fix.
Description
Technical field
The present invention relates to automobile navigation positioning field field, more particularly to a kind of city towards track level navigator fix
Road network model.
Background technology
At present, flourishing for automobile navigation location technology proposes higher requirement to numerical map, traditional road level
Numerical map can not meet intelligent transportation system (ITS Intelligent Transportation System) to positioning
The requirement of precision.Therefore, precision can reach that the track stage enhancement type numerical map of sub-meter grade is extensive by domestic and foreign scholars
Research, track stage enhancement type numerical map is increasingly becoming the important information source of modern vehicle navigation positioning system.
Track stage enhancement type numerical map is to increase some endemic genuses on the basis of original traditional road level numerical map
Property (such as the curvature, the gradient, lane line of road) numerical map, compared to traditional road level numerical map, with more
Abundant geographic information data, more concise rational road network structure.Navigation positioning system can be according to environment and the difference of demand
It is different to increase the information of system needs on the basis of traditional road level numerical map to reach the demand of track level navigator fix.Want structure
Perfect track stage enhancement type numerical map is built, the design of urban road network model is its vital ring.
But most cities road network model is all not perfect in detail enough at present, lacks the data needed for high accuracy positioning
Information, model architecture is excessively single, and data structure redundancy, precision be low and bad adaptability.These deficiencies greatly constrain numeral
The extension of map attribute and the raising of precision.In addition, in the intensive traffic environment of City Building, navigation positioning satellite signal
It can usually be blocked by high building, signal errors is larger, appointing has more satellite to carry out positioning calculation, vehicle can not also realize essence
Really, continue, position in real time.
The content of the invention
In order to solve above-mentioned problem, the present invention proposes a kind of urban road network towards track level navigator fix
Model, the attribute of this model extension traditional road level numerical map, improves the precision of traditional road level numerical map.Multiple
Under miscellaneous urban traffic environment, it can realize that vehicle is accurate, continue, real-time navigation is positioned, meeting the need of track level navigator fix
Ask, for up to this purpose, the present invention proposes a kind of urban road network model towards track level navigator fix, it is characterised in that：
The model carries out segmentation modeling to urban road；By the section between the adjacent intersection of any two and do not wrap
An independent target road is defined as containing intersection, for each target road, its model is by the road of the target road
Road geography information floor, both sides of the road building information floor and the part of road plane lane line Information Level three composition, while the model
In road plane lane line Information Level using three Cardinal Based on Interpolating Spline fit object roads plane lane line,
It can more realistically reflect the plane track present situation of urban road the parameter that obtains；
The model is specific as follows：
The model M is made up of three parts：Road geographic information layer G, both sides of the road building information layer J, road plane car
Diatom Information Level T, i.e.,：
Μ=(G, J, T) (1)；
1) road geographic information layer G：
G=(Rid,O,U,V,W) (2)；
In formula (2), RidRepresent the numbering of target road；The coordinate of target road starting point is represented, wherein
It is the longitude and latitude of starting point respectively with λ；U represents the geographical attribute collection of target road, U=(Re,Rl,Rw), wherein ReRepresent
The title of target road, RlRepresent the length of target road, RwRepresent the width of target road；V represents that target road both sides are built
The numbering collection of thing,Wherein α and β is represented respectively
With the number of right side building on the left of target road,The numbering of i-th of building on the left of expression target road, i=1,
2 ..., α,Represent the numbering of j-th of building on the right side of target road, j=1,2 ..., β；W represents that target road is included
The numbering collection of lane line, W=(N1,…,Nr,…,Nd), wherein d represents the number that target road includes lane line, NrRepresent
The numbering of the r articles lane line in target road, r=1,2 ..., d；
2) both sides of the road building information layer J：
In formula (3), RidThe numbering of target road is represented, α and β represents the number of target road left side and right side building respectively
Mesh,The information of i-th of building on the left of expression target road, i=1,2 ..., α,Represent jth on the right side of target road
The information of individual building, j=1,2 ..., β；It can be further represented as：
In formula (4),The numbering of i-th of building on the left of target road is represented,Represent this
The coordinate of building plane geometry central point,WithRepresent this building plane geometry central point with target track respectively
Road starting point O is east orientation position and ordinate i.e. north orientation position for the abscissa under the Gaussian parabolic line system of origin；Then represent this building plane geometry two end points on target road direction
Coordinate set,It is abscissa of the end points under the Gaussian parabolic line system using target road starting point as origin,It is ordinate of the end points under the Gaussian parabolic line system using target road starting point as origin, HleftRepresent that this builds
Build the height of thing；
Similarly,It can be further represented as：
In formula (5),The numbering of j-th of building on the right side of target road is represented,Represent
The coordinate of this building plane geometry central point,WithRepresent this building plane geometry central point with mesh respectively
Mark road starting point O is east orientation position and ordinate i.e. north orientation position for the abscissa under the Gaussian parabolic line system of origin
Put；Then represent this building plane geometry two on target road direction
The coordinate set of individual end points,It is horizontal seat of the end points under the Gaussian parabolic line system using target road starting point as origin
Mark,It is ordinate of the end points under the Gaussian parabolic line system using target road starting point as origin, HrightRepresent
The height of this building；
3) road plane lane line Information Level T：
In formula (6), RidThe numbering of target road is represented, d represents the number that target road includes lane line, LrRepresent mesh
Mark the information of the r articles lane line on road, wherein r=1,2 ..., d；LrIt can be further represented as：
Lr=(P, Q) (7)；
In formula (7), P={ S1=(x1,y1),…,Sk=(xk,yk),…,Sm=(xm,ym) it is in the r articles lane center
The node coordinate collection sequentially chosen on line, wherein k=2,3 ..., m-2, S2And Sm-1It is the beginning and end in the track, S respectively1
Be on the track extended line with S2A bit adjacent, SmBe on the track extended line with Sm-1A bit adjacent, x and y difference
Be abscissa i.e. east orientation position and ordinate under the Gaussian parabolic line system using target road starting point O as origin i.e.
North orientation position, Q is set of the track using curve obtained parameter after three Cardinal spline interpolations；
4) fitting of terrain vehicle diatom is obtained：
For node coordinate collection P={ S selected on any one lane center in target road1=(x1,
y1),…,Sk=(xk,yk),…,Sm=(xm,ym), it is fitted its horizontal alignment according to three Cardinal Based on Interpolating Spline；
Three Cardinal SPLs are determined that middle two nodes are the end points of curved section, remaining phase by 4 continuous nodes completely
Two adjacent points are used for the slope for calculating the curved section end points；If 4 continuous nodes are Sk-1,Sk,Sk+1,Sk+2, wherein k=
2,3 ..., m-2, if S (μ) is node SkAnd Sk+1Between curved section vector mode, wherein μ be parameter, 0≤μ≤1, then from
Sk-1To Sk+2Between 4 points be used to set up three Cardinal SPL section boundary conditions and be：
In formula (8), S (0) and S (1) is respectively S (μ) in node SkAnd Sk+1Between two end points of curved section position to
Amount, S ' (0) and S ' (1) is respectively tangent vector of the curved section at two-end-point, and curve parameter μ is in two end points values 0 and 1
Between change；Parameter t is the tightness of tension force (tension) coefficient, t control Cardinal SPLs and input node, t
Cardinal SPLs are tight curve during ＞ 0, and Cardinal SPLs are loose curve, the model specification tension force system during t ＜ 0
Number t initial value is 0, and the later stage constantly adjusts t value so that SPL meets target road landform, atural object and surrounding enviroment
Control requirement and required precision；Node S is understood by formula (8)kAnd Sk+1The slope at place respectively with stringWithCheng Zheng
Than；
Four equations in solution formula (8), and it is converted into matrix form, it is as follows：
Cardinal matrixes IcIt is as follows：
Wherein s=1-t/2；
Matrix equation in formula (9) is launched into polynomial form, had：
Further by Sk-1,Sk,Sk+1,Sk+2The component on x on two dimensional surface, y directions is resolved into, node S is obtainedkAnd Sk+1
Between curved section expression formula of three functional expressions of parameter on x, y directions, it is as follows：
Arranged after formula (12) is deployed by μ ascending power, obtain node SkAnd Sk+1Between three Cardinal SPLs
Parametric form, it is as follows：
Parameter is as follows in formula (13)：
Wherein, s=1-t/2；Defined parameters matrix
Simultaneously in node SkAnd Sk+1Between equally spacedly choose 8 nodes, and this 10 nodes are inserted as cubic spline
The interpolation point of value function, and it regard this spline function value as a reference value；Calculate node SkAnd Sk+1Between curved section pass through three times
Deviation between spline function value and a reference value that Cardinal spline methods are obtained, if deviation is just, by t toward negative
Direction is adjusted, if deviation is negative, and t is adjusted toward positive, until by deviation control within 0.3m；
Lane center curve obtained parameter after three Cardinal spline interpolations can be obtained by formula (8)-(14)
Set Q=(t, Y2,…,Yk,…,Ym-2), wherein t is the coefficient of tension, k=2,3 ..., m-2.
Further improvement of the present invention, of length no more than 3km of each pinpoint target road is used due to this model
Gauss Kru＆4＆ger projection is higher in a small range precision, and error can constantly increase with the increase of drop shadow spread, therefore this hair
Of length no more than 3km of selected each pinpoint target road in bright.
A kind of urban road network model towards track level navigator fix proposed by the present invention has the following advantages that：
1st, road plane lane line information is not only contained in model proposed by the present invention, both sides of the road building is also added into
Thing information, road geographic information, road plane lane line information and both sides of the road building information three are merged, weight
New to define urban road network framework, vehicle can be directly using both sides of the road building information in this road net model to receiving
To satellite-signal screened, reject the larger signal of error, reduce resolving amount, it is fixed to be effectively improved on the premise of low cost
Position precision.
2nd, the present invention is using the horizontal alignment in track on three Cardinal Based on Interpolating Spline fit object roads, the sample
Bar curve can preferably adapt to the characteristics of urban road Curvature varying is big, and the parameter of acquisition can more realistically reflect city road
The plane track present situation on road, at the same can directly by change tension force coefficient t value control three Cardinal SPLs with
The tightness of road circuit node, calculates succinct, is easy to control, can preferably meet urban road landform, atural object and road week
Condition for peace is wanted in the control of surrounding environment.
3rd, urban road network model proposed by the present invention, extends the attribute of traditional road level numerical map, improves
The precision of traditional road level numerical map, has the advantages that information content is complete, precision is high, applicability is wide, realizes that vehicle is multiple in city
Accurate under miscellaneous traffic environment, lasting, real-time navigation positioning, meets the demand of track level navigator fix.
Brief description of the drawings
Fig. 1 is model architecture figure of the present invention.
Fig. 2 is road network structure figure of the present invention；By taking the target road of a two-way six-lane as an example, wherein middle part dotted line is represented
Road axis, white dashed line represents each lane center of road, and solid black lines represent both sides of the road boundary line, and rectangle is represented
Road both sides building.
Embodiment
The present invention is described in further detail with embodiment below in conjunction with the accompanying drawings：
The present invention proposes a kind of urban road network model towards track level navigator fix, and its model architecture novelty is closed
Reason, data structure is concisely perfect, extends the attribute of traditional road level numerical map, improves traditional road level numerical map
Precision, has the advantages that information content is complete, precision is high, applicability is wide, under complicated urban traffic environment, realize vehicle it is accurate,
Continue, real-time navigation is positioned, meet the demand of track level navigator fix.
As an embodiment of the present invention, the present invention proposes as depicted in figs. 1 and 2 a kind of towards track level navigator fix
Urban road network model, the model by traditional road level numerical map model architecture and data structure based on, for
The actual demand of track level navigator fix has redefined urban road network framework.The model carries out segmentation to urban road and built
Mould, an independent target road is defined as by the section (not including intersection) between the adjacent intersection of any two,
Because the Gauss Kru＆4＆ger projection that this model is used is higher in a small range precision, and error can be with the increasing of drop shadow spread
Greatly and constantly increase, therefore of length no more than 3km of each pinpoint target road selected in the present invention.
For each target road, its model main road geographic information by the target road layer, both sides of the road are built
Thing Information Level and the part of road plane lane line Information Level three composition are built, while the road plane lane line Information Level in the model
Use the plane lane line of three Cardinal Based on Interpolating Spline fit object roads so that linear with preferably smooth
Property, continuity and plasticity, the SPL can preferably adapt to the characteristics of urban road Curvature varying is big, the parameter of acquisition
The plane track present situation of urban road can more realistically be reflected.Directly it can be controlled simultaneously by change tension force coefficient t value
The tightness of three Cardinal SPLs and road circuit node, calculates succinct, is easy to control, can preferably meet city
Condition for peace is wanted in the control of route topography, atural object and road surrounding enviroment.Urban road network model proposed by the invention, its
Model architecture is new reasonable, and data structure is concisely perfect, extends the attribute of traditional road level numerical map, improves traditional road
The precision of road level numerical map, has the advantages that information content is complete, precision is high, applicability is wide, under complicated urban traffic environment,
Realize that vehicle is accurate, continue, real-time navigation is positioned, meeting the demand of track level navigator fix.
One urban road network model towards track level navigator fix will not only consider road network several in itself
What feature, it is also contemplated that both sides of the road building is blocked to navigation positioning satellite signal, by the information of both sides of the road building
It is added in road net model, realizes road geographic information, road plane lane line information and both sides of the road building information three
Organically blend, be vehicle realize track level navigator fix lay a solid foundation.
Therefore, road network model proposed by the present invention is as follows：
The model M is made up of three parts：Road geographic information layer G, both sides of the road building information layer J, road plane car
Diatom Information Level T, i.e.,
Μ=(G, J, T) (1)；
1st, road geographic information layer G：
G=(Rid,O,U,V,W) (2)；
The Information Level mainly contains the numbering R of target roadid, target road starting point O latitude and longitude coordinates, target track
The geographical attribute collection U on road itself, the numbering collection V of target road both sides building and target road include the numbering collection of lane line
W；As shown in Fig. 2It is the coordinate of target road center line starting point, whereinLongitude, the λ for being starting point be
The latitude and longitude coordinates of this starting point can be carried out geodetic coordinates with Gauss Kru＆4＆ger projection by 3 degree and be tied to height by the latitude of initial point
The conversion of this plane right-angle coordinate, and using this as Gauss Kru＆4＆ger projection origin；U represents the geography of target road
Property set, U=(Re,Rl,Rw), ReRepresent the title of target road, RlRepresent the length of target road, RwRepresent target road
Width；
In addition satellite-signal is blocked in view of target road both sides building, for ease of later stage vehicle location computation to two
Effective extraction of side building information and use, therefore by both sides building independent numbering, so
Wherein α and β represents the number of target road left side and right side building respectively,Represent i-th of building on the left of target road
The numbering of thing, i=1,2 ..., α,Represent the numbering of j-th of building on the right side of target road, j=1,2 ..., β；This model
In lane line refer to the center line in every track in target road, be virtual lane line, do not deposited in real road environment
This lane line is being equal to the track of real road, so W=(N in this model1,…,Nr,…,Nd), wherein d represents mesh
Mark road includes the number of lane line, NrRepresent the numbering of the r articles lane line in target road, r=1,2 ... d；
2nd, both sides of the road building information layer J：
In formula (3), RidThe numbering of target road is represented, α and β represents the number of target road left side and right side building respectively
Mesh,The information of i-th of building on the left of expression target road, i=1,2 ..., α,Represent jth on the right side of target road
The information of individual building, j=1,2 ..., β, this model merges the information of target road one with its both sides building information
Rise.In order in actual vehicle positioning calculation, effectively lock the information of vehicle place both sides of the road building, so needing mesh
The plane geometry center point coordinate and elevation information for marking both sides of the road building are together added in this Information Level, in addition in reality
Urban traffic environment in, target road both sides have many buildings to have very long " span " on road direction, so mould
Type using the coordinate of building plane geometry two end points on target road direction as this building span effective assessment, and
It has been incorporated into this layer.So,It can be further represented as：
In formula (4),The numbering of i-th of building on the left of target road is represented, as shown in Fig. 2
The coordinate of this building plane geometry central point is represented,WithRepresent respectively this building plane geometry central point with
Target road starting point O is the abscissa (east orientation position) under the Gaussian parabolic line system of origin and ordinate (north orientation position
Put),Then represent this building plane geometry two on target road direction
The coordinate set of end points,It is horizontal seat of the end points under the Gaussian parabolic line system using target road starting point as origin
Mark,It is ordinate of the end points under the Gaussian parabolic line system using target road starting point as origin, HleftRepresent
The height of this building；
Similarly,It can be further represented as：
In formula (5),The numbering of j-th of building on the right side of target road is represented, as shown in Fig. 2
The coordinate of this building plane geometry central point is represented,WithRepresent that this building plane geometry central point exists respectively
Abscissa (east orientation position) and ordinate (north orientation under Gaussian parabolic line system by origin of target road starting point O
Position),Then represent this building plane geometry on target road direction
The coordinate set of two end points,It is horizontal stroke of the end points under the Gaussian parabolic line system using target road starting point as origin
Coordinate,It is ordinate of the end points under the Gaussian parabolic line system using target road starting point as origin, HrightTable
Show the height of this building；The specific data message of target road and its both sides building can from OpenStreetMap,
The Bureau of Urban Planning in the Map Services such as Google Earth software or location obtains；
3rd, road plane lane line Information Level T：
In formula (6), RidThe numbering of target road is represented, d represents the number that target road includes lane line, LrRepresent mesh
Mark the information of the r articles lane line on road, wherein r=1,2 ..., d；LrIt can be further represented as：
Lr=(P, Q) (7)；
In formula (7), P={ S1=(x1,y1),…,Sk=(xk,yk),…,Sm=(xm,ym) it is in the r articles lane center
The node coordinate collection sequentially chosen on line, wherein k=2,3 ..., m-2, S2And Sm-1It is the beginning and end in the track, S respectively1
Be on the track extended line with S2A bit adjacent, SmBe on the track extended line with Sm-1A bit adjacent, x and y difference
It is abscissa (east orientation position) and ordinate under the Gaussian parabolic line system using target road starting point O as origin
(north orientation position), Q is set of the track using curve obtained parameter after three Cardinal spline interpolations；
4th, the fitting of terrain vehicle diatom is obtained：
In general, the curve for track horizontal alignment on fit object road needs to pass through or closely track
Node, and the curve is required to the characteristics of adaptation urban road Curvature varying is big, disclosure satisfy that urban road landform, atural object
And condition for peace is wanted in the control of road surrounding enviroment, the plane track present situation of urban road can be reflected, while parameter of curve meter
Calculate succinct, be easy to practical application.Conventional curve-fitting method has Lagrange's interpolation, least square interpolation method, divided at present
Duan Sanci Hermite's interpolation methods and cubic spline interpolation etc..Wherein Lagrange's interpolation is simply easily realized, but can be gone out
Existing dragon lattice phenomenon, and error of fitting is larger；Least square interpolation method is relatively adapted to for rambling unordered discrete point, but
It is not ideal enough for orderly point；Three Hermite's interpolation methods of segmentation combine the derivative value of function, compared with Lagrange's interpolation
Method precision increases, but slickness is inadequate；The interpolation curve that cubic spline interpolation is obtained is by all in target road
Node, and line smoothing, conformal function are also preferable, but required interstitial content is more, calculate numerous and diverse, are not suitable for actual answer
With.
In order to solve drawbacks described above, come present invention employs three Cardinal Based on Interpolating Spline in fit object road
The horizontal alignment in every track.The curve that this method is obtained passes through all nodes in track in target road, linear to have preferably
Slickness, continuity and plasticity, while the tightness that can adjust curve according to different specification criterion reach and meet city
The SPL of city's target road requirement so that the SPL can preferably adapt to the big spy of urban road Curvature varying
Point, the parameter of acquisition can more realistically reflect the plane track present situation of urban road, and required interstitial content is limited, meter
Calculate succinct, be easy to practical application.
For the node coordinate collection P={ S chosen in order on any one lane center in target road1=(x1,
y1),…,Sk=(xk,yk),…,Sm=(xm,ym), it is fitted its horizontal alignment according to three Cardinal Based on Interpolating Spline；
Three Cardinal SPLs are determined that middle two nodes are the end points of curved section, remaining phase by 4 continuous nodes completely
Two adjacent points are used for the slope for calculating the curved section end points；If 4 continuous nodes are Sk-1,Sk,Sk+1,Sk+2, wherein k=
2,3 ..., m-2, if S (μ) is node SkAnd Sk+1Between curved section vector mode, wherein μ be parameter, 0≤μ≤1, then from
Sk-1To Sk+2Between 4 points be used to set up three Cardinal SPL section boundary conditions and be：
In formula (8), S (0) and S (1) is respectively S (μ) in node SkAnd Sk+1Between curved section two end points position to
Amount, S ' (0) and S ' (1) is respectively tangent vector of the curved section at two-end-point, and the parameter μ of curve is in two end points values 0
And change between 1；Parameter t is the elastic journey of tension force (tension) coefficient, t control Cardinal SPLs and input node
Degree, Cardinal SPLs are tight curve during t ＞ 0, and Cardinal SPLs are loose curve during t ＜ 0, when t is 0,
Cardinal battens are also known as Catmull-Rom battens or Overhauser battens, model specification coefficient of tension t initial value
For 0, the later stage constantly adjusts t value so that SPL meets the control requirement of target road landform, atural object and surrounding enviroment
And required precision；Node S is understood by formula (8)kAnd Sk+1The slope at place respectively with stringWithIt is directly proportional；
Four equations in solution formula (8), and it is converted into matrix form, it is as follows：
Cardinal matrixes IcIt is as follows：
Wherein s=1-t/2；
Matrix equation in formula (9) is launched into polynomial form, had：
Further by Sk-1,Sk,Sk+1,Sk+2The component on x on two dimensional surface, y directions is resolved into, node S is obtainedkAnd Sk+1
Between curved section expression formula of three functional expressions of parameter on x, y directions, it is as follows：
Arranged after formula (12) is deployed by μ ascending power, obtain node SkAnd Sk+1Between three Cardinal SPLs
Parametric form, it is as follows：
Parameter is as follows in formula (13)：
Wherein, s=1-t/2；Defined parameters matrix
Simultaneously in node SkAnd Sk+1Between equally spacedly choose 8 nodes, and this 10 nodes are inserted as cubic spline
The interpolation point of value function, the interpolation curve precision obtained by the method is higher, more the target road lane line of approaching to reality,
And it regard this spline function value as a reference value.Calculate node SkAnd Sk+1Between curved section inserted by three Cardinal battens
Deviation between spline function value and a reference value that value method is obtained, if deviation is just, t is adjusted toward negative direction, if partially
Difference is negative, then adjusts t toward positive, until by deviation control within 0.3m；
Lane center curve obtained parameter after three Cardinal spline interpolations can be obtained by formula (8)-(14)
Set Q=(t, Y2,…,Yk,…,Ym-2), wherein t is the coefficient of tension, k=2,3 ..., m-2.
The above described is only a preferred embodiment of the present invention, being not the limit for making any other form to the present invention
System, and any modification made according to technical spirit of the invention or equivalent variations, still fall within model claimed of the invention
Enclose.
Claims (2)
1. a kind of urban road network model towards track level navigator fix, it is characterised in that：
The model carries out segmentation modeling to urban road；By the section between the adjacent intersection of any two and not comprising friendship
The cross road mouthful is defined as an independent target road, for each target road, its model by the target road road
Information Level, both sides of the road building information layer and the part of road plane lane line Information Level three composition are managed, while in the model
Road plane lane line Information Level uses the plane lane line of three Cardinal Based on Interpolating Spline fit object roads, to obtain
The parameter taken can more realistically reflect the plane track present situation of urban road；
The model is specific as follows：
The model M is made up of three parts：Road geographic information layer G, both sides of the road building information layer J, road plane lane line
Information Level T, i.e.,：
Μ=(G, J, T) (1)；
1) road geographic information layer G：
G=(Rid,O,U,V,W) (2)；
In formula (2), RidRepresent the numbering of target road；The coordinate of target road starting point is represented, whereinAnd λ
It is the longitude and latitude of starting point respectively；U represents the geographical attribute collection of target road, U=(Re,Rl,Rw), wherein ReRepresent mesh
Mark the title of road, RlRepresent the length of target road, RwRepresent the width of target road；V represents target road both sides building
Numbering collection,Wherein α and β represents target respectively
With the number of right side building on the left of road,The numbering of i-th of building on the left of expression target road, i=1,2 ..., α,Represent the numbering of j-th of building on the right side of target road, j=1,2 ..., β；W represents that target road includes lane line
Numbering collection, W=(N1,…,Nr,…,Nd), wherein d represents the number that target road includes lane line, NrRepresent target track
The numbering of Lu Shang r bar lane lines, r=1,2 ..., d；
2) both sides of the road building information layer J：
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</msub>
<mo>,</mo>
<msubsup>
<mi>F</mi>
<mrow>
<mi>l</mi>
<mi>e</mi>
<mi>f</mi>
<mi>t</mi>
</mrow>
<mi>l</mi>
</msubsup>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msubsup>
<mi>F</mi>
<mrow>
<mi>l</mi>
<mi>e</mi>
<mi>f</mi>
<mi>t</mi>
</mrow>
<mi>i</mi>
</msubsup>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msubsup>
<mi>F</mi>
<mrow>
<mi>l</mi>
<mi>e</mi>
<mi>f</mi>
<mi>t</mi>
</mrow>
<mi>&alpha;</mi>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>F</mi>
<mrow>
<mi>r</mi>
<mi>i</mi>
<mi>g</mi>
<mi>h</mi>
<mi>t</mi>
</mrow>
<mi>l</mi>
</msubsup>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msubsup>
<mi>F</mi>
<mrow>
<mi>r</mi>
<mi>i</mi>
<mi>g</mi>
<mi>h</mi>
<mi>t</mi>
</mrow>
<mi>j</mi>
</msubsup>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<msubsup>
<mi>F</mi>
<mrow>
<mi>r</mi>
<mi>i</mi>
<mi>g</mi>
<mi>h</mi>
<mi>t</mi>
</mrow>
<mi>&beta;</mi>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mi>&alpha;</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mi>&beta;</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
In formula (3), RidThe numbering of target road is represented, α and β represents the number of target road left side and right side building respectively,The information of i-th of building on the left of expression target road, i=1,2 ..., α,Represent to build for j-th on the right side of target road
Build the information of thing, j=1,2 ..., β；It can be further represented as：
<mrow>
<msubsup>
<mi>F</mi>
<mrow>
<mi>l</mi>
<mi>e</mi>
<mi>f</mi>
<mi>t</mi>
</mrow>
<mi>i</mi>
</msubsup>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>E</mi>
<mrow>
<mi>l</mi>
<mi>e</mi>
<mi>f</mi>
<mi>t</mi>
</mrow>
<mi>i</mi>
</msubsup>
<mo>,</mo>
<msub>
<mi>C</mi>
<mrow>
<mi>l</mi>
<mi>e</mi>
<mi>f</mi>
<mi>t</mi>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>D</mi>
<mrow>
<mi>l</mi>
<mi>e</mi>
<mi>f</mi>
<mi>t</mi>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>H</mi>
<mrow>
<mi>l</mi>
<mi>e</mi>
<mi>f</mi>
<mi>t</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
In formula (4),The numbering of i-th of building on the left of target road is represented,Represent that this builds
The coordinate of object plane geometric center point,WithRepresent that this building plane geometry central point rises with target road respectively
Initial point O is east orientation position and ordinate i.e. north orientation position for the abscissa under the Gaussian parabolic line system of origin；Then represent this building plane geometry two end points on target road direction
Coordinate set,It is abscissa of the end points under the Gaussian parabolic line system using target road starting point as origin,It is ordinate of the end points under the Gaussian parabolic line system using target road starting point as origin, HleftRepresent that this builds
Build the height of thing；
Similarly,It can be further represented as：
<mrow>
<msubsup>
<mi>F</mi>
<mrow>
<mi>r</mi>
<mi>i</mi>
<mi>g</mi>
<mi>h</mi>
<mi>t</mi>
</mrow>
<mi>j</mi>
</msubsup>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>E</mi>
<mrow>
<mi>r</mi>
<mi>i</mi>
<mi>g</mi>
<mi>h</mi>
<mi>t</mi>
</mrow>
<mi>j</mi>
</msubsup>
<mo>,</mo>
<msub>
<mi>C</mi>
<mrow>
<mi>r</mi>
<mi>i</mi>
<mi>g</mi>
<mi>h</mi>
<mi>t</mi>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>D</mi>
<mrow>
<mi>r</mi>
<mi>i</mi>
<mi>g</mi>
<mi>h</mi>
<mi>t</mi>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>H</mi>
<mrow>
<mi>r</mi>
<mi>i</mi>
<mi>g</mi>
<mi>h</mi>
<mi>t</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
In formula (5),The numbering of j-th of building on the right side of target road is represented,Represent that this builds
The coordinate of object plane geometric center point is built,WithRepresent this building plane geometry central point with target track respectively
Road starting point O is east orientation position and ordinate i.e. north orientation position for the abscissa under the Gaussian parabolic line system of origin；Then represent this building plane geometry two ends on target road direction
The coordinate set of point,It is abscissa of the end points under the Gaussian parabolic line system using target road starting point as origin,It is ordinate of the end points under the Gaussian parabolic line system using target road starting point as origin, HrightRepresent this
The height of building；
3) road plane lane line Information Level T：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>T</mi>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>R</mi>
<mrow>
<mi>i</mi>
<mi>d</mi>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>L</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msub>
<mi>L</mi>
<mi>r</mi>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msub>
<mi>L</mi>
<mi>d</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>r</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mi>d</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
In formula (6), RidThe numbering of target road is represented, d represents the number that target road includes lane line, LrRepresent target track
The information of Lu Shang r bar lane lines, wherein r=1,2 ..., d；LrIt can be further represented as：
Lr=(P, Q) (7)；
In formula (7), P={ S1=(x1,y1),…,Sk=(xk,yk),…,Sm=(xm,ym) it is on the r articles lane center
The node coordinate collection that order is chosen, wherein k=2,3 ..., m-2, S2And Sm-1It is the beginning and end in the track, S respectively1Be
With S on the track extended line2A bit adjacent, SmBe on the track extended line with Sm-1It is adjacent a bit, x and y be respectively
The abscissa under Gaussian parabolic line system by origin of target road starting point O is east orientation position and ordinate i.e. north orientation
Position, Q is set of the track using curve obtained parameter after three Cardinal spline interpolations；
4) fitting of terrain vehicle diatom is obtained：
For node coordinate collection P={ S selected on any one lane center in target road1=(x1,y1),…,Sk=
(xk,yk),…,Sm=(xm,ym), it is fitted its horizontal alignment according to three Cardinal Based on Interpolating Spline；Three Cardinal
SPL is determined that middle two nodes are the end points of curved section by 4 continuous nodes completely, and remaining two adjacent point is used
In the slope for calculating the curved section end points；If 4 continuous nodes are Sk-1,Sk,Sk+1,Sk+2, wherein k=2,3 ..., m-2, if
S (μ) is node SkAnd Sk+1Between curved section vector mode, wherein μ be parameter, 0≤μ≤1, then from Sk-1To Sk+2Between 4
Point is used to set up three Cardinal SPL section boundary conditions：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>S</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>S</mi>
<mi>k</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>S</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mi>S</mi>
<mo>&prime;</mo>
</msup>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>*</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mi>S</mi>
<mo>&prime;</mo>
</msup>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>*</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>S</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
In formula (8), S (0) and S (1) is respectively S (μ) in node SkAnd Sk+1Between two end points of curved section position vector, S '
(0) it is respectively tangent vector of the curved section at two-end-point with S ' (1), curve parameter μ is between two end points values 0 and 1
Change；Parameter t is the tightness of tension force (tension) coefficient, t control Cardinal SPLs and input node, t ＞ 0
When Cardinal SPLs be tight curve, Cardinal SPLs are loose curve, the model specification coefficient of tension t during t ＜ 0
Initial value be 0, the later stage constantly adjusts t value so that SPL meets target road landform, atural object and surrounding enviroment
Control is required and required precision；Node S is understood by formula (8)kAnd Sk+1The slope at place respectively with stringWithCheng Zheng
Than；
Four equations in solution formula (8), and it is converted into matrix form, it is as follows：
<mrow>
<mi>S</mi>
<mrow>
<mo>(</mo>
<mi>&mu;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>&lsqb;</mo>
<mtable>
<mtr>
<mtd>
<msup>
<mi>&mu;</mi>
<mn>3</mn>
</msup>
</mtd>
<mtd>
<msup>
<mi>&mu;</mi>
<mn>2</mn>
</msup>
</mtd>
<mtd>
<mi>&mu;</mi>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
<mo>&rsqb;</mo>
<msub>
<mi>I</mi>
<mi>c</mi>
</msub>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>S</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>S</mi>
<mi>k</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>S</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>S</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Cardinal matrixes IcIt is as follows：
<mrow>
<msub>
<mi>I</mi>
<mi>c</mi>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mi>s</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mn>2</mn>
<mo>-</mo>
<mi>s</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>s</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</mtd>
<mtd>
<mi>s</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>2</mn>
<mi>s</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>s</mi>
<mo>-</mo>
<mn>3</mn>
</mrow>
</mtd>
<mtd>
<mrow>
<mn>3</mn>
<mo>-</mo>
<mn>2</mn>
<mi>s</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mi>s</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mi>s</mi>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mi>s</mi>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Wherein s=1-t/2；
Matrix equation in formula (9) is launched into polynomial form, had：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<mi>S</mi>
<mrow>
<mo>(</mo>
<mi>&mu;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mo>-</mo>
<msup>
<mi>s&mu;</mi>
<mn>3</mn>
</msup>
<mo>+</mo>
<mn>2</mn>
<msup>
<mi>s&mu;</mi>
<mn>2</mn>
</msup>
<mo>-</mo>
<mi>s</mi>
<mi>&mu;</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>S</mi>
<mi>k</mi>
</msub>
<mo>&lsqb;</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>-</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
<msup>
<mi>&mu;</mi>
<mn>3</mn>
</msup>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>-</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
<msup>
<mi>&mu;</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mn>1</mn>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>+</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&lsqb;</mo>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>-</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
<msup>
<mi>&mu;</mi>
<mn>3</mn>
</msup>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>-</mo>
<mn>2</mn>
<mi>s</mi>
<mo>)</mo>
</mrow>
<msup>
<mi>&mu;</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>s</mi>
<mi>&mu;</mi>
<mo>&rsqb;</mo>
<mo>+</mo>
<msub>
<mi>S</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msup>
<mi>s&mu;</mi>
<mn>3</mn>
</msup>
<mo>-</mo>
<msup>
<mi>s&mu;</mi>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Further by Sk-1,Sk,Sk+1,Sk+2The component on x on two dimensional surface, y directions is resolved into, node S is obtainedkAnd Sk+1Between
Expression formula of three functional expressions of parameter of curved section on x, y directions is as follows：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mi>&mu;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>&lsqb;</mo>
<mtable>
<mtr>
<mtd>
<msup>
<mi>&mu;</mi>
<mn>3</mn>
</msup>
</mtd>
<mtd>
<msup>
<mi>&mu;</mi>
<mn>2</mn>
</msup>
</mtd>
<mtd>
<mi>&mu;</mi>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
<mo>&rsqb;</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mi>s</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mn>2</mn>
<mo>-</mo>
<mi>s</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>s</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</mtd>
<mtd>
<mi>s</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>2</mn>
<mi>s</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>s</mi>
<mo>-</mo>
<mn>3</mn>
</mrow>
</mtd>
<mtd>
<mrow>
<mn>3</mn>
<mo>-</mo>
<mn>2</mn>
<mi>s</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mi>s</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mi>s</mi>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mi>s</mi>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>x</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>x</mi>
<mi>k</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>x</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>x</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>y</mi>
<mrow>
<mo>(</mo>
<mi>&mu;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>&lsqb;</mo>
<mtable>
<mtr>
<mtd>
<msup>
<mi>&mu;</mi>
<mn>3</mn>
</msup>
</mtd>
<mtd>
<msup>
<mi>&mu;</mi>
<mn>2</mn>
</msup>
</mtd>
<mtd>
<mi>&mu;</mi>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
<mo>&rsqb;</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mi>s</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mn>2</mn>
<mo>-</mo>
<mi>s</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>s</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</mtd>
<mtd>
<mi>s</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>2</mn>
<mi>s</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>s</mi>
<mo>-</mo>
<mn>3</mn>
</mrow>
</mtd>
<mtd>
<mrow>
<mn>3</mn>
<mo>-</mo>
<mn>2</mn>
<mi>s</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mi>s</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mi>s</mi>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mi>s</mi>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>y</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>y</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>y</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>&le;</mo>
<mi>&mu;</mi>
<mo>&le;</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>2</mn>
<mo>,</mo>
<mn>3</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mi>m</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Arranged after formula (12) is deployed by μ ascending power, obtain node SkAnd Sk+1Between three Cardinal SPLs ginseng
Number form formula is as follows：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mi>&mu;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mi>A</mi>
<mn>0</mn>
<mi>k</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>A</mi>
<mn>1</mn>
<mi>k</mi>
</msubsup>
<mi>&mu;</mi>
<mo>+</mo>
<msubsup>
<mi>A</mi>
<mn>2</mn>
<mi>k</mi>
</msubsup>
<msup>
<mi>&mu;</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<msubsup>
<mi>A</mi>
<mn>3</mn>
<mi>k</mi>
</msubsup>
<msup>
<mi>&mu;</mi>
<mn>3</mn>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>y</mi>
<mrow>
<mo>(</mo>
<mi>&mu;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mi>B</mi>
<mn>0</mn>
<mi>k</mi>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>B</mi>
<mn>1</mn>
<mi>k</mi>
</msubsup>
<mi>&mu;</mi>
<mo>+</mo>
<msubsup>
<mi>B</mi>
<mn>2</mn>
<mi>k</mi>
</msubsup>
<msup>
<mi>&mu;</mi>
<mn>2</mn>
</msup>
<mo>+</mo>
<msubsup>
<mi>B</mi>
<mn>3</mn>
<mi>k</mi>
</msubsup>
<msup>
<mi>&mu;</mi>
<mn>3</mn>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>&le;</mo>
<mi>&mu;</mi>
<mo>&le;</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>2</mn>
<mo>,</mo>
<mn>3</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mi>m</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Parameter is as follows in formula (13)：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>A</mi>
<mn>0</mn>
<mi>k</mi>
</msubsup>
<mo>=</mo>
<msub>
<mi>x</mi>
<mi>k</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>A</mi>
<mn>1</mn>
<mi>k</mi>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>sx</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>sx</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>A</mi>
<mn>2</mn>
<mi>k</mi>
</msubsup>
<mo>=</mo>
<mn>2</mn>
<msub>
<mi>sx</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>-</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
<msub>
<mi>x</mi>
<mi>k</mi>
</msub>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>-</mo>
<mn>2</mn>
<mi>s</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>x</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>sx</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>A</mi>
<mn>3</mn>
<mi>k</mi>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>sx</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>-</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>x</mi>
<mi>k</mi>
</msub>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>-</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
<msub>
<mi>x</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>sx</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>B</mi>
<mn>0</mn>
<mi>k</mi>
</msubsup>
<mo>=</mo>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>B</mi>
<mn>1</mn>
<mi>k</mi>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>sy</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>sy</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>B</mi>
<mn>2</mn>
<mi>k</mi>
</msubsup>
<mo>=</mo>
<mn>2</mn>
<msub>
<mi>sy</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>-</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>-</mo>
<mn>2</mn>
<mi>s</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>y</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>sy</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>B</mi>
<mn>3</mn>
<mi>k</mi>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>sy</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>-</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>-</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
<msub>
<mi>y</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>sy</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>14</mn>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Wherein, s=1-t/2；Defined parameters matrix
Simultaneously in node SkAnd Sk+1Between equally spacedly choose 8 nodes, and regard this 10 nodes as cubic spline interpolation letter
Several interpolation points, and it regard this spline function value as a reference value；Calculate node SkAnd Sk+1Between curved section pass through three times
Deviation between spline function value and a reference value that Cardinal spline methods are obtained, if deviation is just, by t toward negative
Direction is adjusted, if deviation is negative, and t is adjusted toward positive, until by deviation control within 0.3m；
Lane center curve obtained parameter sets Q after three Cardinal spline interpolations can be obtained by formula (8)-(14)
=(t, Y2,...,Yk,...,Ym-2), wherein t is the coefficient of tension, k=2,3 ..., m-2.
2. a kind of urban road network model towards track level navigator fix according to claim 1, it is characterised in that：
Of length no more than 3km of each pinpoint target road.
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| CN110162903A (en) * | 2019-05-28 | 2019-08-23 | 辽宁师范大学 | A kind of urban architecture windward side density calculating method and system parallel based on grid |
| CN112784533A (en) * | 2021-02-07 | 2021-05-11 | 腾讯科技（深圳）有限公司 | Lane group number generation method, lane group number generation device, computer equipment and storage medium |
| CN113064077A (en) * | 2021-02-20 | 2021-07-02 | 山东科技大学 | Lithium battery life attenuation curve fitting method based on piecewise fitting |
| CN114771518A (en) * | 2022-04-06 | 2022-07-22 | 北京百度网讯科技有限公司 | Method and device for generating lane center guiding line, electronic equipment and medium |
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