CN103592665B - Car-mounted terminal positioning track approximating method based on B-spline curves - Google Patents
Car-mounted terminal positioning track approximating method based on B-spline curves Download PDFInfo
- Publication number
- CN103592665B CN103592665B CN201310578766.3A CN201310578766A CN103592665B CN 103592665 B CN103592665 B CN 103592665B CN 201310578766 A CN201310578766 A CN 201310578766A CN 103592665 B CN103592665 B CN 103592665B
- Authority
- CN
- China
- Prior art keywords
- mrow
- msub
- msubsup
- mfrac
- mtr
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
Landscapes
- Engineering & Computer Science (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Computer Networks & Wireless Communication (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Peptides Or Proteins (AREA)
- Complex Calculations (AREA)
Abstract
The present invention discloses a kind of car-mounted terminal positioning track approximating method based on B-spline curves, the positioning track of car-mounted terminal is fitted using B-spline curves, so as to reach and the more preferable fitting degree of actual vehicle driving trace, matched curve has good smooth effect, and has to local position sampling point tolerance certain control and filtering feature.This method uses three rank B-spline algorithms, because during the traveling of vehicle, the collecting quantity of location data is more, and the amount of calculation higher than the B-spline algorithm of three ranks can be very big, and smooth effect of the B-spline algorithm at node less than three ranks is again poor.There is three rank B-spline algorithms second order to lead continuous characteristic and the application on actual the vehicle driving trace more identical and smaller suitable engineering of amount of calculation at the node of line segment.
Description
Technical field
The invention belongs to field of satellite navigation, and in particular to a kind of car-mounted terminal positioning track based on B-spline curves is intended
Conjunction method.
Background technology
There are many equipment (positioning terminal such as car-mounted terminal, mobile phone terminal) mostly to possess based on GNSS at present
The function of (Global Navigation Satellite System, GPS) satellite fix.
The fitting of positioning vehicle-carried terminal-pair vehicle driving trace, generally by with the position of certain frequency acquisition vehicle
Information, then drawn by these positional information calculations gathered and approximate continuously drive track.This process can be regarded as
Continuous function is mended on the basis of discrete data, by value situation of the function at limited point, function is estimated in other points
The approximation at place, i.e. interpolation or fit procedure.Traditional vehicle driving trace is calculated, and typically has two methods：
The first is the linear interpolation method of discrete point, and this method is simply discrete positional information sampled point foundation
The sequencing of collection is attached by straight line, and what is obtained is the broken polygonal line by each sampled point.This method is existed
Various disadvantages：First, the actual motion track of vehicle impossible linear running completely between two sampled points, with two samplings
The interval of point is longer, and bend error of the actual running orbit of vehicle just between the straight line of 2 points of formation is also bigger, and if
Need the precision for improving calculating track then to reduce the interval of sampling, be also accomplished by more processing times and memory space.
Secondly, the vehicle position information obtained by locating module, the reason for by various environmental factors in vehicle moving process
It there may be certain error, that is to say, that positional information sampled point also occurs to be existed partially with actual vehicle driving trace
Difference, thus the method for directly carrying out line, the statistical property progress filtration treatment according to track sampled point, indivedual not abnormal
The value of sampled point will produce considerable influence to whole piece fitting track, and error is also just difficult to avoid that.
Second is to carry out transition by the discrete points data to collection, forms the shifting that a curve carrys out approximate location terminal
Dynamic rail mark, i.e., nonlinear interpolation or approximating method.At present in engineering with being more widely polynomial interopolation or fitting,
This method can reduce the error between interpolation or matched curve and actual path curve to a certain extent, but to interpolation
Or the requirement of fitting function is higher, often kissed with node (collection point) polygon (polygon that adjacent node is connected by straight line)
Close higher its smoothness of curve just poor, it is again poor with the polygonal degree of agreement of node for the higher curve of smoothness.Cause
How this controls non-linear interpolation or fitting function so that the curve between discrete point can more coincide the moving rail of positioning terminal
Mark, is just particularly important.
The content of the invention
Therefore, for it is above-mentioned the problem of, the present invention propose it is a kind of based on B-spline curves car-mounted terminal positioning track fitting
Method, its algorithm is simple and curve matching effect is good.
In order to solve the above-mentioned technical problem, thinking of the present invention is that car-mounted terminal is determined using B-spline curves
Position track is fitted, so as to reach with the more preferable fitting degree of actual vehicle driving trace, matched curve there is good put down
Sliding effect, and have certain control and filtering feature to local position sampling point tolerance.This method is calculated using three rank B-splines
Method, because during the traveling of vehicle, the collecting quantity of location data is more, higher than the calculating of the B-spline algorithm of three ranks
Amount can be very big, and smooth effect of the B-spline algorithm at node less than three ranks is again poor.Three rank B-spline algorithms are in line segment
There is second order to lead continuous characteristic at node more to coincide and the smaller suitable engineering of amount of calculation with actual vehicle driving trace
On application.
Specifically, a kind of car-mounted terminal positioning track approximating method based on B-spline curves of the present invention, including following step
Suddenly：
Step 1:According to the recursive definition of B-spline, the point of k rank B-spline curves is expressed as follows：
And
Wherein t is parameter, PiFor i-th of control point of B-spline curves；ujFor the vector at j-th of control point in B-spline curves
Value, it determines parameter t span；Pi (l)For B-spline curves section the l times recursive process in ratio quantile, it by
Determined in the l-1 times recursive processPi (l)Two ratio quantile passing ratio valuesWithCalculate and；
Make the k=3 in formula (1), it is known that i value is j-2, j-1, j, j+1, j+2, that is, determines one section of three rank B-spline
Curved section needs 4 control points：Pj-2、Pj-1、Pj、Pj+1, and each control point vector value uj-2、uj-1、uj、uj+1(each control point
Vector value t span is determined, in order that t span is consistent during recurrence calculation, order)；
Step 2:
Determine the vector value u at each control pointi, i=0,1,2,3...n, namely parameter t span.The arrow at control point
What value was preferably monotonically changed, because if choose when and increase, when and the vector value of reduction, then can cause at same parameters value
Curve is not unique difficult.The knot vector value assignment mode of B-spline can have many kinds, for the ease of calculating and realizing, false
If the number of positional information sampled point is n, the present invention carries out assignment with equation below to control point vector：
Step 3：The positional information sampled point of car-mounted terminal is arranged according to time order and function order, and is used as B-spline
Each control point P of matched curvei, i=0,1,2,3...n, lighted from the 1st control and take continuous 4 sampled points in order
It is used as 4 control point P for calculating one section of 3 rank B-spline curvesj-2、Pj-1、Pj、Pj+1, utilize Pj-2、Pj-1Calculate first time recursion
Ratio quantile curveUtilize Pj-1、PjCalculate the ratio quantile curve of first time recursionUtilize Pj、
Pj+1Calculate the ratio quantile curve of first time recursionIts expression formula difference is as follows：
Step 4：Utilize the ratio quantile curve calculated in step 3Calculate second recursion
Ratio quantile curveUtilize the ratio quantile curve calculated in step 3Calculate second
The ratio quantile curve of recursionIts expression formula difference is as follows：
Step 5：Utilize the ratio quantile curve calculated in step 4Calculate third time recursion
Ratio quantile curveThe definition of B-spline in step 1It is by control point Pj-2、Pj-1、Pj、Pj+1
The B-spline curves P (t) of generation, its expression formula is as follows：
Step 6：Ensuing 4 control points are taken to calculate next section of B-spline curves, repeat step 3 and step 5 in order
Process, until sampled point between all B-spline curves Duan Douyi calculate finish；
Step 7：May be not enough for the multiple of sampled point total number for 4, the i.e. control point of final stage B-spline curves
The situation of 4, can be supplemented along the control point for moving to the last period B-spline curves；
Step 8：Combine the expression formula of all B-spline curves sections, you can obtain the B-spline curves of a continuous and derivable, should
Curve is with actual positioning terminal running orbit by with good fitting degree.
Car-mounted terminal positioning track approximating method based on B-spline curves, by the generating principle and B-spline of B-spline curves
Property be used in and positional information is gathered by positioning terminal be fitted in the technical process of vehicle driving trace.Compared to traditional
Track of vehicle computational methods, the present invention mainly has following improvement：
First, the vehicle location track that generates of the present invention is curve, due in vehicle actual moving process, two positions
It is not often linear running between sampled point, so of the invention have with traditional method for carrying out discrete points interpolation by straight line
There is more preferable track degree of agreement.In addition, for the track of vehicle of linear running, computational methods of the invention same can also be obtained
To the fitting track of straight line；
Second, compared to vehicle driving trace obtained from other carry out interpolation arithmetics by positional information sampled point, sheet
Invention is the process being fitted by B-spline curves to discrete positional information sampled point.Enter line position in on-vehicle positioning terminal
In confidence breath gatherer process, due to there is the factors such as position error and environmental disturbances, position sampling point information inherently has necessarily
Error also not all on vehicle driving trace, and the process that B-spline curves are fitted is to a certain extent to sampled point
Information has carried out filtering process, and obtained fitting track has more preferable smoothness compared with Interpolation Process, and error is also just smaller；It is existing
There is technology also to have what is carried out curve fitting by polynomial interopolation, interpolation is that the curve of interpolation is to pass through with the difference being fitted
Each sampled point, and the curve being fitted tend not to by all sampled point (special circumstances, sampled point is arranged in a line,
This fitting is overlapped with interpolation).This method describes B-spline curves fit procedure, meanwhile, the matched curve master of cubic B-spline
There are two advantages, (1) can have with node (sampled point) polygon (adjacent node is connected the polygon to be formed by straight line)
Preferable degree of agreement, i.e., higher with actual path degree of agreement, (2) matched curve has good smooth degree, and node
Locate to lead for Second Order Continuous, this is more conform with the rule of vehicle movement.And often during fitting of a polynomial, it is polygon to node
The smoothness of its high curve of shape degree of agreement will be deteriorated, high its of line smoothing degree to the polygonal degree of agreement of node just
It is relatively low.It is a relatively good equalization point that B-spline Curve, which is fitted within fitting of a polynomial,；
3rd, compared to other nonlinear curve or fitting of a polynomial processes, the present invention use three rank B-spline curves pair
The driving trace of on-vehicle positioning terminal is fitted, and track of vehicle is all more conform with the degree of agreement and smoothness of curve
Practical application scene；
4th, the present invention introduces the computational methods by control point vector value in implementation process, passes through different controls
Point vector assignment processed can carry out a certain degree of adjustment to the B-spline curves of generation, in engineering with more preferable flexibility ratio from
And it is adapted to the application under more multi-environment.
Brief description of the drawings
Fig. 1 is to pass through the design sketch that straight line carries out track fitting in the prior art；
Fig. 2 carries out the design sketch of track fitting for the present invention by B-spline curves；
Fig. 3 is the driving trace design sketch obtained in the prior art by interpolation arithmetic；
Fig. 4 is the driving trace design sketch obtained by B-spline curves fitting operation of the invention；
Fig. 5 is the B-spline curves that control point vector value etc. is distributed generation；
Fig. 6 has the B-spline curves that multiplicity is generated for two ends control point vector value.
Embodiment
In conjunction with the drawings and specific embodiments, the present invention is further described.
Present invention movement of positioning terminal in order that the curve between the positional information sampled point of collection can more coincide
Track, its driving trace is fitted using B-spline curves.B-spline curves are a kind of special representation forms of polynomial curve, are passed through
The fitting that curve carries out vehicle driving trace has more preferable smoothness, also just more conforms to shifting of the vehicle under transport condition
Dynamic rail mark.Further, since B-spline curves have good local property, during vehicle running orbit is fitted, even if individual
The error do not sampled is larger, and the influence to matched curve is also simply local to produce influence to overall, that is to say, that make
There is good statistical property and filter action with the fit procedure of B-spline curves.
Specifically, a kind of car-mounted terminal positioning track approximating method based on B-spline curves of the present invention, including following step
Suddenly：
Step 1:According to the dBool recursive definitions of B-spline, the point on one section of k rank B-spline curves is expressed as follows：
And
Wherein t is parameter, PiFor i-th of control point of B-spline curves, ujFor the vector at j-th of control point in B-spline curves
Value, it determines parameter t span, Pi (l)For B-spline curves section the l times recursive process in ratio quantile, it by
Determined in the l-1 times recursive processPi (l)Two ratio quantile passing ratio valuesWithCalculate and.
Make the k=3 in formula (1), it is known that one section of 3 rank B-spline curves needs 4 control points, i.e. i value for j-2, j-1, j, j+1,
j+2。
Step 2:The positional information sampled point of car-mounted terminal is arranged according to time order and function order and intended as B-spline
Close each control point P of curvei(i=0,1,2,3...n), and the vector value u at each control point is determinedi(i=0,1,2,3...n),
The vector value at control point will actually be used for limiting parameter t span, and the shape of influence curve to a certain extent.No
Increase when should choose, when and the vector value of reduction, in order to avoid cause at same parameters value curve not unique difficult, therefore control
The vector value of system point should be monotonically changed.Assuming that the number of positional information sampled point is n, the present invention is with equation below to control
Point vector carries out assignment：
A certain degree of adjustment can be carried out to the B-spline curves of generation by different control point vector assignment, in work
There is more preferable flexibility ratio in journey to adapt to the application under more multi-environment.The different assignment modes of vector value can be in certain journey
The shape of B-spline curves is influenceed on degree, the present invention carries out assignment using formula (2) to control point vector, simple easily to realize, and can
Suitable for application generally；
Step 3：Lighted from the 1st control and take continuous 4 sampled points bent as one section of 3 rank B-spline is calculated in order
4 control point P of linej-2、Pj-1、Pj、Pj+1, then in conjunction with formula (1) and formula (2), utilize Pj-2、Pj-1Calculate and pass for the first time
The ratio quantile curve pushed awayUtilize Pj-1、PjCalculate the ratio quantile curve of first time recursionUtilize Pj、
Pj+1Calculate the ratio quantile curve of first time recursionIts expression formula difference is as follows：
Step 4：With reference to formula (1) and formula (2), the ratio quantile curve calculated in step 3 is utilizedCalculate the ratio quantile curve of second of recursionUtilize the ratio point position calculated in step 3
Point curveCalculate the ratio quantile curve of second of recursionIts expression formula difference is as follows：
Step 5：With reference to formula (1) and formula (2), the ratio quantile curve calculated in step 4 is utilizedCalculate the ratio quantile curve of third time recursionFrom the definition of B-splineAs
By control point Pj-2、Pj-1、Pj、Pj+1The B-spline curves P (t) of generation, its expression formula is as follows：
Step 6：Ensuing 4 control points are taken to calculate next section of B-spline curves, repeat step 3 and step 5 in order
Process, until sampled point between all B-spline curves Duan Douyi calculate finish；
Step 7：May be not enough for the multiple of sampled point total number for 4, the i.e. control point of final stage B-spline curves
The situation of 4, can be supplemented along the control point for moving to the last period B-spline curves；
Step 8：Combine the expression formula of all B-spline curves sections, you can obtain the B-spline curves of a continuous and derivable, should
Curve is with actual positioning terminal running orbit by with good fitting degree.
The present invention uses the car-mounted terminal positioning track approximating method based on B-spline curves, and the generation of B-spline curves is former
The property of reason and B-spline is used in be gathered positional information to be fitted in the technical process of vehicle driving trace by positioning terminal.
Compared to traditional track of vehicle computational methods, mainly there is following improvement：
First, the vehicle location track that generates of the present invention is curve, due in vehicle actual moving process, two positions
It is not often linear running between sampled point, so of the invention have with traditional method for carrying out discrete points interpolation by straight line
There is more preferable track degree of agreement.Fig. 1 carries out the effect of track fitting for traditional method for carrying out discrete points interpolation by straight line
Fruit is schemed, and Fig. 2 is the design sketch that track fitting is carried out by B-spline curves of the invention.In addition, for the vehicle rail of linear running
Mark, computational methods of the invention can also be similarly obtained the fitting track of straight line.
Second, compared to vehicle driving trace obtained from other carry out interpolation arithmetics by positional information sampled point, sheet
Invention is the process being fitted by B-spline curves to discrete positional information sampled point.Interpolation and fitting difference be,
The track of interpolation calculation will pass through each position sampled point, and the track being fitted is that each sampled point is approached in global level.
Enter in on-vehicle positioning terminal in row positional information gatherer process, due to there is the factors such as position error and environmental disturbances, position is adopted
Sampling point information inherently has certain error also not all on vehicle driving trace, and the process that B-spline curves are fitted
Filtering process is carried out to sampling point information to a certain extent, obtained fitting track has preferably smooth compared with Interpolation Process
Degree, error is also just smaller.Fig. 3 is the driving trace design sketch obtained in the prior art by interpolation arithmetic, and Fig. 4 is the present invention
The driving trace design sketch obtained by B-spline curves fitting operation.Meanwhile, matched curve is generally without going past each
Individual node (sampled point), and the curve of interpolation can necessarily pass through each sampled point, it is therefore to be understood that the process of process of fitting treatment,
There is provided data message to node (sampled point) to a certain extent to be filtered, i.e., some differ greatly with whole-sample point trend
Sampled point its provide information be weakened.Above-mentioned algorithm is the process that three rank B-spline curves are fitted, thus to adopting
Sampling point information has carried out filtering process, also just because of this filtering process, the matched curve made more smoothes out light than interpolation curve
It is sliding, also more meet vehicle running orbit, it is seen that Fig. 3 and Fig. 4 contrast.
3rd, the present invention introduces the computational methods by control point vector value in implementation process, passes through different controls
Point vector assignment processed can carry out a certain degree of adjustment to the B-spline curves of generation, in engineering with more preferable flexibility ratio from
And it is adapted to the application under more multi-environment.Fig. 5 is that the distribution (adjacent two point vectors difference is consistent) such as control point vector value is raw
Into B-spline curves, Fig. 6 has the B-spline curves that multiplicity is generated for two ends control point vector value.
Although specifically showing and describing the present invention with reference to preferred embodiment, those skilled in the art should be bright
In vain, do not departing from the spirit and scope of the present invention that appended claims are limited, in the form and details can be right
The present invention makes a variety of changes, and is protection scope of the present invention.
Claims (2)
1. a kind of car-mounted terminal positioning track approximating method based on B-spline curves, it is characterised in that：Comprise the following steps：
Step 1:According to the recursive definition of B-spline, the point of k rank B-spline curves is expressed as follows：
And
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>P</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>=</mo>
<msub>
<mi>P</mi>
<mi>i</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>P</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<msubsup>
<mi>a</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<msubsup>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>a</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>)</mo>
</mrow>
</msubsup>
<msubsup>
<mi>P</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>a</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>l</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mo>=</mo>
<mfrac>
<mrow>
<mi>t</mi>
<mo>-</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mi>k</mi>
<mo>-</mo>
<mi>l</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<mi>l</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mi>k</mi>
<mo>,</mo>
<mi>i</mi>
<mo>=</mo>
<mi>j</mi>
<mo>-</mo>
<mi>k</mi>
<mo>+</mo>
<mi>l</mi>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<mi>j</mi>
<mo>,</mo>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
<mo>;</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein t is parameter, PiFor i-th of control point of B-spline curves；ujFor the vector value at j-th of control point in B-spline curves, it
Determine parameter t span；Pi (l)For the ratio quantile in B-spline curves the l times recursive process of section, it is by l-1
Determined in secondary recursive processPi (l)Two ratio quantile passing ratio valuesWithCalculate and；
Make the k=3 in formula (1), it is known that i value is j-2, j-1, j, j+1, j+2, that is, determines one section of three rank B-spline curves
Section needs 4 control points：Pj-2、Pj-1、Pj、Pj+1, and each control point vector value uj-2、uj-1、uj、uj+1；
Step 2:Determine the vector value u at each control pointi, i=0,1,2,3...n, and the vector value u at each control pointiTo be monotonically changed
's；
Step 3：The positional information sampled point of car-mounted terminal is arranged according to time order and function order, and is fitted as B-spline
Each control point P of curvei, i=0,1,2,3...n, lighted from the 1st control and take continuous 4 sampled point conducts in order
Calculate 4 control point P of one section of 3 rank B-spline curvesj-2、Pj-1、Pj、Pj+1, utilize Pj-2、Pj-1Calculate the ratio of first time recursion
Example quantile curveUtilize Pj-1、PjCalculate the ratio quantile curve of first time recursionUtilize Pj、Pj+1Meter
Calculate the ratio quantile curve of first time recursionIts expression formula difference is as follows：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>P</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>t</mi>
<mo>-</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<msub>
<mi>P</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<mi>t</mi>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<msub>
<mi>P</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>P</mi>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>t</mi>
<mo>-</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<msub>
<mi>P</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>-</mo>
<mi>t</mi>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<msub>
<mi>P</mi>
<mi>j</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>P</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>t</mi>
<mo>-</mo>
<msub>
<mi>u</mi>
<mi>j</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>3</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mi>j</mi>
</msub>
</mrow>
</mfrac>
<msub>
<mi>P</mi>
<mi>j</mi>
</msub>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>3</mn>
</mrow>
</msub>
<mo>-</mo>
<mi>t</mi>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>3</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mi>j</mi>
</msub>
</mrow>
</mfrac>
<msub>
<mi>P</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<mi>t</mi>
<mo>&Element;</mo>
<mo>&lsqb;</mo>
<msub>
<mi>u</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>;</mo>
</mrow>
Step 4：Utilize the ratio quantile curve calculated in step 3Calculate the ratio of second of recursion
Quantile curveUtilize the ratio quantile curve calculated in step 3 Calculate second recursion
Ratio quantile curveIts expression formula difference is as follows：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>P</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>t</mi>
<mo>-</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<msubsup>
<mi>P</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<mi>t</mi>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<msubsup>
<mi>P</mi>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>P</mi>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>t</mi>
<mo>-</mo>
<msub>
<mi>u</mi>
<mi>j</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mi>j</mi>
</msub>
</mrow>
</mfrac>
<msubsup>
<mi>P</mi>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>-</mo>
<mi>t</mi>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mi>j</mi>
</msub>
</mrow>
</mfrac>
<msubsup>
<mi>P</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<mi>t</mi>
<mo>&Element;</mo>
<mo>&lsqb;</mo>
<msub>
<mi>u</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>;</mo>
</mrow>
Step 5：Utilize the ratio quantile curve calculated in step 4Calculate the ratio of third time recursion
Quantile curveFrom the definition of B-splineIt is by control point Pj-2、Pj-1、Pj、Pj+1The B-spline of generation
Curve P (t), its expression formula is as follows：
<mrow>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msubsup>
<mi>P</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>t</mi>
<mo>-</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>3</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<msubsup>
<mi>P</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>3</mn>
</mrow>
</msub>
<mo>-</mo>
<mi>t</mi>
</mrow>
<mrow>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>3</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<msubsup>
<mi>P</mi>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mi>t</mi>
<mo>&Element;</mo>
<mo>&lsqb;</mo>
<msub>
<mi>u</mi>
<mi>j</mi>
</msub>
<mo>,</mo>
<msub>
<mi>u</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&rsqb;</mo>
<mo>;</mo>
</mrow>
Step 6：Ensuing 4 control points are taken to calculate the mistake of next section of B-spline curves, repeat step 3 and step 5 in order
Journey, until all B-spline curves Duan Douyi between sampled point are calculated and finished；
Step 7：May be inadequate 4 for the multiple of sampled point total number for 4, the i.e. control point of final stage B-spline curves
Situation, can be supplemented along the control point that move to the last period B-spline curves；
Step 8：Combine the expression formula of all B-spline curves sections, you can obtain the B-spline curves of a continuous and derivable, the curve
With actual positioning terminal running orbit by with good fitting degree.
2. according to a kind of car-mounted terminal positioning track approximating method based on B-spline curves of claim 1, it is characterised in that：Institute
State in step 2, the vector u at control pointiAssignment is carried out according to following formula：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>u</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mi>i</mi>
<mo>&Element;</mo>
<mo>&lsqb;</mo>
<mn>0</mn>
<mo>,</mo>
<mn>3</mn>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>u</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mi>i</mi>
<mo>,</mo>
<mi>i</mi>
<mo>&Element;</mo>
<mo>&lsqb;</mo>
<mn>4</mn>
<mo>,</mo>
<mi>n</mi>
<mo>-</mo>
<mn>4</mn>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>u</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mn>0</mn>
<mo>,</mo>
<mi>i</mi>
<mo>&Element;</mo>
<mo>&lsqb;</mo>
<mi>n</mi>
<mo>-</mo>
<mn>3</mn>
<mo>,</mo>
<mi>n</mi>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>.</mo>
</mrow>
2
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201310578766.3A CN103592665B (en) | 2013-11-15 | 2013-11-15 | Car-mounted terminal positioning track approximating method based on B-spline curves |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201310578766.3A CN103592665B (en) | 2013-11-15 | 2013-11-15 | Car-mounted terminal positioning track approximating method based on B-spline curves |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN103592665A CN103592665A (en) | 2014-02-19 |
| CN103592665B true CN103592665B (en) | 2017-09-22 |
Family
ID=50082875
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201310578766.3A Active CN103592665B (en) | 2013-11-15 | 2013-11-15 | Car-mounted terminal positioning track approximating method based on B-spline curves |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN103592665B (en) |
Families Citing this family (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104517032A (en) * | 2014-12-02 | 2015-04-15 | 华中科技大学 | Fitting method of data points based on B-spline curve and device |
| US10066947B2 (en) * | 2015-10-30 | 2018-09-04 | Faraday & Future Inc. | Methods and apparatus for improved precision street maps using low cost sensors |
| CN108268960B (en) * | 2016-12-30 | 2023-06-02 | 法法汽车(中国)有限公司 | Driving track optimizing system |
| WO2019104581A1 (en) * | 2017-11-30 | 2019-06-06 | 深圳市大疆创新科技有限公司 | Track generating method and apparatus, and unmanned ground vehicle |
| CN108182330A (en) * | 2018-01-15 | 2018-06-19 | 南京理工大学 | A kind of method that the response of flexible rectangular thin plate Rigid-flexible Coupling Dynamics is calculated based on B-spline |
| CN111208807A (en) * | 2018-11-06 | 2020-05-29 | 苏州艾吉威机器人有限公司 | AGV motion control method based on B spline curve |
| CN113635296B (en) * | 2021-06-30 | 2022-09-27 | 苏州艾吉威机器人有限公司 | Method for tracking arbitrary curve path |
| CN114184206B (en) * | 2021-12-03 | 2024-04-19 | 北京车慧达科技有限公司 | Method and device for generating driving route based on vehicle track points |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2010073432A1 (en) * | 2008-12-24 | 2010-07-01 | 株式会社ソニー・コンピュータエンタテインメント | Image processing device and image processing method |
| CN102998684B (en) * | 2012-11-21 | 2016-12-21 | 厦门雅迅网络股份有限公司 | A kind of terminal positioning track fitting method based on Bezier |
-
2013
- 2013-11-15 CN CN201310578766.3A patent/CN103592665B/en active Active
Also Published As
| Publication number | Publication date |
|---|---|
| CN103592665A (en) | 2014-02-19 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN103592665B (en) | Car-mounted terminal positioning track approximating method based on B-spline curves | |
| CN102998684B (en) | A kind of terminal positioning track fitting method based on Bezier | |
| CN110160541A (en) | Reconstructing method and device, storage medium, the electronic device of motion profile | |
| CN110595475A (en) | Tracking path fitting method and device, intelligent automobile and storage medium | |
| CN108549378B (en) | Mixed path planning method and system based on grid map | |
| CN106646518B (en) | GPS track Supplementing Data method based on three rank Beziers and interpolation | |
| CN106840175B (en) | Method and device for matching vehicle running track with road network | |
| CN104699956B (en) | A kind of main line green wave coordination effect evaluation method based on mobile terminal | |
| CN110095127A (en) | A kind of hidden Markov model map-matching method based on segmentation | |
| CN105606102B (en) | Grid model based PDR indoor positioning method and system | |
| CN108090838A (en) | Identify method, apparatus, server, client and the system of damaged vehicle component | |
| CN106767851B (en) | The collected tracing point of positioning system is matched to the method and device thereof of map | |
| CN108973997A (en) | Running rail determination device and servomechanism | |
| CN103471589A (en) | Method for identifying walking mode and tracing track of pedestrian in room | |
| CN105551239B (en) | travel time prediction method and device | |
| CN106871924A (en) | A kind of VMT Vehicle-Miles of Travel computational methods based on satellite positioning signal | |
| CN111158365A (en) | Path planning method and device, robot and storage medium | |
| CN104615889A (en) | Intelligent vehicle path tracking method and system based on clothoid following | |
| CN109064741A (en) | The method of trunk road vehicle running track reconstruct based on multisource data fusion | |
| CN105933857B (en) | A kind of mobile terminal locations prediction technique and device | |
| CN111177934B (en) | Method, apparatus and storage medium for reference path planning | |
| CN111126598B (en) | Automatic parking method, automatic parking device, computer equipment and storage medium | |
| CN111814286B (en) | Lane-level map geometric model building method for automatic driving | |
| CN108180921A (en) | Utilize the AR-HUD navigation system and its air navigation aid of GPS data | |
| CN103218915A (en) | Experience route generation method based on probe vehicle data |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |