CN111145599B - Curve flight segment and error distribution establishing method - Google Patents

Curve flight segment and error distribution establishing method Download PDF

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CN111145599B
CN111145599B CN201911305458.7A CN201911305458A CN111145599B CN 111145599 B CN111145599 B CN 111145599B CN 201911305458 A CN201911305458 A CN 201911305458A CN 111145599 B CN111145599 B CN 111145599B
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flight
curve
segment
aircraft
error
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CN111145599A (en
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张建平
谢方泉
邹翔
吴卿刚
陈振玲
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Second Research Institute of CAAC
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    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G5/00—Traffic control systems for aircraft, e.g. air-traffic control [ATC]
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Abstract

The invention provides a method for determining a curve flight segment, which comprises the steps of S1, establishing a flight segment curve model; s2 returning to simulate the flight; s3 estimating the lateral flight error distribution of the flight segment; s4 estimating the vertical flight error distribution of the leg. The method utilizes a large amount of sample data to fit the flight section curve through a statistical analysis technology, analyzes the flight errors, establishes the aircraft flight error distribution matched with the corresponding spatial position of the aircraft in the air route, improves the accuracy of the aircraft collision assessment, is particularly suitable for the complex situation of the aircraft curve climbing stage or the situation of flight turning, and is a great improvement of the safety risk assessment.

Description

Curve flight segment and error distribution establishing method
Technical Field
The invention relates to the technical field of air traffic management.
Background
The collision risk assessment is one of the most important works of the safety bottom line of civil aviation security, the risk essentially occurs randomly, and the possibility of risk occurrence cannot be radically avoided. For the international civil aviation organization, the concept of safe target level is provided for the air traffic collision risk (the collision frequency of each pair of airplanes is 5 multiplied by 10)-9Sub/flight hour), different scholars also try to measure the risk of collision from various aspects, with the aim of reasonably judging whether the air traffic system meets the requirements of the safety target level, determining the safety interval between aircrafts, etc. The core of collision risk assessment is the establishment of flight errors, which generally involve three dimensions of longitudinal errors, lateral errors and vertical errors, and the existing method focuses on macroscopic analysis and has insufficient precision for some microscopic scenes. For example:
1. the existing straight line model of the flight path of the aircraft is mostly adopted to evaluate the collision risk, and the model is not applicable when the aircraft turns.
2. A great deal of research assumes that the flight errors of the aircraft meet fixed distribution in a section of a flight segment, and although the calculation of collision risk assessment is facilitated, certain loss is caused to the risk assessment precision.
Based on this, a reasonable aircraft flight trajectory curve model is a great improvement for improving the accuracy of collision risk assessment, and is particularly applied to the stage of entering and leaving the aircraft. Meanwhile, the distribution of the aircraft flight errors related to the corresponding spatial positions in the aircraft flight trajectory is more accurate, and is particularly important when analyzing micro scenes such as the climbing and landing of the aircraft.
Disclosure of Invention
The purpose of the invention is: aiming at the technical defect that the curve flight leg of the existing aircraft lacks error analysis, the invention utilizes a large amount of sample data to fit the leg curve through a statistical analysis technology, analyzes the flight errors, establishes the aircraft flight error distribution matched with the corresponding spatial position of the aircraft in the airway, improves the accuracy of aircraft collision assessment, and is particularly suitable for the complex situation of the aircraft curve climbing stage or the situation of flight turning.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the invention comprises the following steps:
a method for determining a curved flight segment comprises the following steps:
s1, establishing a flight path curve model;
s2 returning to simulate the flight;
s3 estimating the lateral flight error distribution of the flight segment;
s4 estimating the vertical flight error distribution of the leg.
Preferably, the S1 establishes a flight path curve model, including:
flight segment curve l(s) ═ x(s), y (s)), including length l0Straight line of radius r1Central angle of alpha1Arc, radius position r of2Angular position of centre of circle alpha2Arc of (d), slope k ═ tan (α)1-α2) A straight line of (a);
the mathematical expression of l(s) ═ x(s), y (s)) is:
Figure BDA0002322161450000021
Figure BDA0002322161450000022
wherein l0＝x0，l1＝x0+r1α1，l2＝x0+r1α1+r2α2，
x2＝x0+r1sinα1+r2(sinα1-sin(α1-α2))
y2＝y0+r1(1-cosα1)-r2(cosα1-cos(α1-α2))
L(s) is defined by the parameter (x)0，y0，r1，α1，r2，α2) And (4) uniquely determining.
Preferably, the S2 regression model segment includes:
s201 note diIs a sample point (X)i，Yi) The distance to the leg L, i.e.:
Figure BDA0002322161450000023
where inf represents the infimum bound of the set of real numbers
S202, optimizing an objective function LS (x) by using a least square method0，y0，r1，α1，r2，α2)，
Figure BDA0002322161450000024
The obtained parameter (x)0，y0，r1，α1，r2，α2) Best fit parameters for curve l(s);
s203, the best fitting parameters are brought into the formula (1) and the formula (2), and a mathematical expression of L (S) is obtained.
Preferably, the S3 estimating the leg lateral flight error distribution includes:
s301, taking the step length as delta S, and dividing the flight segment curve into sub-flight segments Li＝L(s)，s∈[i×Δs，(i+1)×Δs]Assume each sub-flight segment LiWith inner points correspondingLateral flight error epsilony(s) all satisfy a standard deviation of σiNormal distribution of (i), i.e. for any s e [ i x Δ s, (i +1) x Δ s]，εy(s)～N(0，σi) Where σ isiIs the standard deviation;
the normal plane nplane (S) of the curve of the flight segment of S302 is:
Figure BDA0002322161450000031
Figure BDA0002322161450000032
is a vertical unit vector of the unit,
Figure BDA0002322161450000033
normal vector for curve L(s);
obtaining a parameter sigma by using sample points between nplane (i × Δ s) and nplane ((i +1) × Δ s) and adopting a maximum likelihood estimation methodiThe parameter estimation value of (2);
s303 compares the parameter sigmaiIs introduced into epsilony(s)～N(0，σi) Obtaining the lateral flight error epsilon of the flight segment L(s)y(s) distribution function.
Preferably, the S4 estimating the vertical flight error distribution of the leg includes:
s401 for a given S, the actual position of the flight z (S) should be predicted from zintend(s) and systematic flight errors by aircraft
Figure BDA0002322161450000034
Composition is carried out;
assuming aircraft system errors
Figure BDA0002322161450000035
Predicted position zintend(s) obey a uniform distribution over a certain interval, i.e.: z is a radical ofintend(s)～U[z1(s)，z2(s)](ii) a Get zintend(s) the median line generated is the leg, then the vertical flight error due to uncertainty in the predicted trajectory
Figure BDA0002322161450000036
Satisfies the distribution U < -z [ ]0(s)，z0(s)]Suppose that
Figure BDA0002322161450000037
And system flight error
Figure BDA0002322161450000038
Independent of each other, then random vectors
Figure BDA0002322161450000039
Has a joint probability density function of
Figure BDA00023221614500000310
So epsilonz(s) a probability density function p (x) of:
Figure BDA00023221614500000311
wherein the function erf (x) is referred to as the error function of x, defined as:
Figure BDA00023221614500000312
s402 for each segment LiUsing sample point drive-in (6) between nplane (i × Δ s) and nplane ((i +1) × Δ s), sample data adopts maximum likelihood estimation method to estimate parameters
Figure BDA0002322161450000041
S403, parameter
Figure BDA0002322161450000042
The parameter estimation value belt (6) obtains the vertical flight error epsilon of the flight section L(s)zProbability density function p (x) of(s).
The invention has the beneficial effects that:
1. the curve flight segment establishing method is suitable for the complex situation of the curve climbing stage of the aircraft or the situation of flight turning, and is a great improvement on safety risk assessment.
2. The method for establishing the curve flight segment overcomes the defects that in the prior art, the flight errors of the aircraft are assumed to totally meet fixed distribution macroscopically, certain loss is caused to the precision of risk assessment, and the utilization of airspace resources cannot be greatly economical.
3. The flight error distribution adopted by the method is related to the corresponding spatial position of the aircraft in the air route, and is crucial to the analysis of the climbing and landing of the aircraft.
Drawings
The invention is further illustrated with reference to the following figures and examples.
FIG. 1 is a schematic view of a flight profile model;
FIG. 2 is a schematic view of parameters corresponding to a flight leg collision risk zone boundary;
FIG. 3 is a graph of the effect of curve fitting for a flight segment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
The sections are all civil aviation aircraft flight sections, and the section collision risk area is an area which guarantees that the collision probability of the civil aviation aircraft and the unmanned aerial vehicle is smaller than a designated target safety level e and is determined according to the flight errors of the civil aviation aircraft. If the unmanned plane flies outside the area, the probability of collision between the unmanned plane and the civil aircraft flying in the corresponding flight segment is less than e, and the unmanned plane is considered to be an acceptable safety risk.
The invention discloses a technology for determining the boundary of a collision risk area by fitting a flight path curve and analyzing flight errors through a statistical analysis technology on the basis of supposing that a large amount of sample data is obtained. The data source processed by the invention comes from the air traffic control unit running air traffic control unitAutomated system whose data format meets the asterix cat62 format specification, assuming that based on the off-site program dep, we acquire enough sample points pi＝(xi，yi，zi)。
S1 flight curve modeling
The method mainly aims at the problem of modeling the flight section curve in the take-off and landing stages, through observation of a large amount of data in the early stage, the generality is not lost, and the flight section L is assumed (the flight section is considered at this moment)
Figure BDA0002322161450000053
Projection on a horizontal plane) is formed by splicing a straight line and a circular arc continuous first derivative. As shown in fig. 1, the leg curve may be composed of the following parts:
a first part of length l0Has an end point of (x)0，y0)；
A second portion having a radius r1With a central angle of alpha1Arc of (d) (turning arc);
third part, radius position r2Angular position of center of circle alpha2Arc of (arc of correcting excessive turning)
A fourth part having a slope k of tan (α)1-α2) Is measured.
The precise mathematical description of the model corresponding to the flight curve l(s) (x(s), y (s)) is:
Figure BDA0002322161450000051
Figure BDA0002322161450000052
wherein l0＝x0，l1＝x0+r1α1，l2＝x0+r1α1+r2α2，
x2＝x0+r1sinα1+r2(sinα1-sin(α1-α2))
y2＝y0+r1(1-cosα1)-r2(cosα1-cos(α1-α2))
Model of the flight segment is composed of parameter x0，y0，r1，α1，r2，α2And (4) determining. When the parameters are specialized, the model covers the normal condition when alpha is2When the angle is 0, the turning is accurate; when alpha is1＝α2When 0, the case corresponds to a straight flight.
S2 route segment L regression fitting
Note diExpressed as sample points (X)i，Yi) The distance to the leg L, i.e.:
Figure BDA0002322161450000061
taking a target optimization objective function:
Figure BDA0002322161450000062
the obtained parameter (x)0，y0，r1，α1，r2，α2) Is the best fit parameter of the curve. Therefore, through the analysis, the specific form l(s) of the flight segment can be obtained from the actually acquired sample data.
S3 lateral error εy(s) analysis
The foregoing steps have fitted the flight segment l(s) with the collected data points, which are now analyzed for flight errors. Taking the step length as delta s, and dividing the flight segment L into sub-flight segments Li＝L(s)，s∈[i×Δs，(i+1)×Δs]Assume each sub-flight segment LiThe lateral errors corresponding to each point in the interior all meet the standard deviation of sigmaiNormal distribution of (i), i.e. for any s e [ i x Δ s, (i +1) x Δ s]The method comprises the following steps:
εy(s)～N(0，σi)
obtaining a parameter sigma by using sample points between nplane (i × Δ s) and nplane ((i +1) × Δ s) and adopting a maximum likelihood estimation methodiThe parameter estimation of (2).
The principle of the maximum likelihood estimation method is that a sample observed value (x) is fixed1，x2，...，xn) Choosing the parameter theta to make L (x)1，x2，...，xn；θ)＝max L(x1，x2，...，xn(ii) a Theta) obtained in this way is related to the sample value, theta (x)1，x2，...，xn) Maximum likelihood estimate called parameter theta, its corresponding statistic theta (X)1，X2，...，Xn) Referred to as the maximum likelihood estimator of theta. Using ln L (θ) as an increasing function of L (θ), so ln L (θ) and L (θ) reach maximum at the same point, and then taking logarithm to the likelihood function L (θ), using differential knowledge to convert into solving log-likelihood equation:
Figure BDA0002322161450000063
the stationary point obtained by solving the equation is the solved maximum point, so that the maximum likelihood estimation value of the parameter can be obtained.
S4 vertical error epsilonz(s) analysis
Since the positions of the aircraft taking off the runway are not the same, assuming that the expected trajectory of the aircraft follows a certain uniform distribution, for a given s the actual position z(s) of the aircraft should be derived from its expected position zintend(s) and systematic flight errors by aircraft
Figure BDA00023221614500000714
The invention assumes aircraft systematic flight errors, which are the deviations of the actual and predicted positions of the aircraft, which are inevitably caused by various causes when the aircraft travels along the predicted trajectory
Figure BDA0002322161450000071
Figure BDA0002322161450000072
zintend(s) obey a uniform distribution over a certain interval, i.e.: z is a radical ofintend(s)～U[z1(s)，z2(s)]. Get zintend(s) the resulting centerline is the leg, then the error due to uncertainty in the predicted trajectory
Figure BDA0002322161450000073
Satisfies the distribution U < -z [ ]0(s)，z0(s)]Suppose that
Figure BDA0002322161450000074
And system flight error
Figure BDA0002322161450000075
Independent of each other, then random vectors
Figure BDA0002322161450000076
Has a joint probability density function of
Figure BDA0002322161450000077
So epsilonz(s) a probability density function p (x) of:
Figure BDA0002322161450000078
wherein the function erf (x) is referred to as the error function of x, defined as:
Figure BDA0002322161450000079
according to the method, each segment L is divided intoiEstimating parameters by using sample data by maximum likelihood estimation method
Figure BDA00023221614500000710
To obtain epsilonz(s) distribution function.
S5 collision risk zone boundary determination
As shown in fig. 2, the flight
Figure BDA00023221614500000711
s∈[0，s1]Corresponding collision risk zone rz(s)1) Is one of
Figure BDA00023221614500000712
s∈[0，s1]The boundary of the inner three-dimensional area is composed of the following parts:
rear vertical surface bsf(s)1): i.e. normal plane of curve L(s) at the starting point
bsf(s1)＝nplane(0)
Left vertical face lsf(s)1): a vertical surface located on the left side of the curve L and having equal distance to each point on the curve L, i.e. a vertical surface with a curve
Figure BDA00023221614500000713
Being vertical faces of the base
Figure BDA0002322161450000081
Right vertical side rsf(s)1): a vertical plane located at the right side of the horizontal projection curve L(s) and having equal distance from each point on L, i.e. a curve
Figure BDA0002322161450000082
Being vertical faces of the base
Figure BDA0002322161450000083
Front vertical plane fsf(s)1): including a horizontal projection curve L(s) at a point L(s)1) Plane of treatment
fsf(s1)＝nplane(s0)
A bottom surface ssf(s)1): perpendicular to the left vertical surface and the right vertical surface and the track curve
Figure BDA0002322161450000084
Parallel curved surfaces
Figure BDA0002322161450000085
Zone rz(s) at risk of collision1) The rear vertical surface bsf(s) is described1) Left vertical face lsf(s)1) Right vertical surface rsf(s)1) Front vertical plane fsf(s)1) Bottom surface ssf(s)1) Enclosed as comprising
Figure BDA00023221614500000810
And the inner three-dimensional area is a core area for limiting the operation of the unmanned aerial vehicle.
Assuming a lateral error epsilon of the actual flight path of the aircraft at point L(s)y(s) vertical error εz(s)，Fy(s，εy) Is the lateral error εy(s) distribution function, Fz(s，εz) Is a vertical error epsilonz(s) distribution function, e is acceptable collision probability, and the collision risk zone corresponding to the flight curve is the minimum zone satisfying the following conditions:
the first condition is as follows: the maximum side width of the aircraft in the flight section is assumed to be 2 lambdayThen the left and right vertical plane parameters dl、drIt should satisfy:
Figure BDA0002322161450000086
Figure BDA0002322161450000087
Figure BDA0002322161450000088
wherein P (x) is the probability of occurrence of event x, Fy(s，εy) Is a lateral error distribution function, epsilony(s) is the lateral error;
and a second condition: the maximum height of the aircraft in the section is assumed to be 2 lambdazThen the floor parameters should satisfy:
Figure BDA0002322161450000089
P(εz(s)＜-dz+λz)＝Fz(s，-dz+λz)≤e
wherein P (x) is the probability of occurrence of event x, Fz(s，εz) Is a function of the vertical error distribution, epsilonz(s) is the vertical error;
parameter d which in fact satisfies the two conditions mentioned abovel，dr，dzThere are an infinite number of reasons for any parameter dlIf the above condition is satisfied, d is knownl+1 still satisfies the condition;
the invention calls the parameter d satisfying the above two conditionsl，dr，dzFor e risk avoidance, the parameter d of e risk avoidance is usedl，dr，dzAre respectively represented as RAl(e)，RAr(e)，RAz(e) Then, the parameters corresponding to the collision risk zone boundary are respectively:
dl＝infRAl(e)
dr＝infRAr(e)
dz＝infRAz(e)
wherein: inf represents the infimum boundary of the real number set;
dlis the flight path curve and the left vertical plane lsf(s)1) The distance between them;
dzis the curve of the flight section and the bottom surface ssf(s)1) The distance between them;
dris the curve of the flight segment and the right vertical plane rsf(s)1) The distance between them.
The first embodiment is as follows:
collecting operation data of a certain airport, extracting the data and recording a three-dimensional space coordinate position (theta, phi, h), wherein the (theta, phi) is respectively corresponding latitude and longitude, and the h is height and has the unit of feet.
The longitude and latitude of the reference point of the airport are (N294308, E1063829), the corresponding orientation of the runway is a true angle of 17 degrees, and the altitude of the airport is h01364 feet, the radius of the earth for this city is about R6377830 meters, and the radian system of the latitude and longitude corresponding to the computed airport reference point is expressed as:
θ0＝0.6186924
φ0＝1.8612433
then it is known that a coordinate transformation should be performed along the runway direction:
x＝R(φ-φ0)sin(β)cos(θ0)+(θ-θ0)Rcos(β)
y＝R(φ-φ0)cos(β)cos(θ0)-(θ-θ0)Rsin(β)
according to the knowledge of differential geometry and calculus, within 50 kilometers of the airport periphery, the longitude error delta theta is less than 50000/R and less than 0.008, and the Taylor expansion is adopted
cosθ＝cos(θ0)-sin(θ0)Δθ+O(Δθ)2
The accuracy of coordinate transformation in the 50KM category around the airport is greater than 99%.
Obtain a sample point PiCartesian coordinates (X)i，Yi) Using a sample (X)i，Yi) To determine model parameters (x)0，y0，r1，α1，r2，α2). Sample point (X)i，Yi) Distance d from the curveiThe calculation process of (2) is as follows:
Figure BDA0002322161450000101
minimizing LS (x)0，y0，r1，α1，r2，alpha2) The parameter results obtained were:
(3748.91714，2018.654，7830.656，0.3684，24117.5824，0.112529)
thus, the parameters 3748.91714, 2018.654, 7830.656, 0.3684, 24117.5824, 0.112529) obtained are the best fit parameters for the curve, the above fitting effect being shown in fig. 3.
The second embodiment: collision risk zone setting under certain airport approach procedure
The corresponding flight segment of the partial runway departure procedure is a curve (the situation that the flight takes a turn in the process of taking off). Corresponding leg in this example
Figure BDA0002322161450000106
s∈[0，10000]Comprises the following steps:
Figure BDA0002322161450000102
Figure BDA0002322161450000103
z(s)＝0.05s
the flight segment describes the arc turning angle of 6 km along the radius after taking off for 2 km
Figure BDA0002322161450000104
And then the straight-line flight is continued. In this example, it is still assumed that the flight side error εy(s) obeys the same distribution as the above example and assumes εz(s) a probability density function p (x) of:
Figure BDA0002322161450000105
wherein the function erf (x) is referred to as the error function of x, defined as:
Figure BDA0002322161450000111
Figure BDA0002322161450000112
according to the constraint condition one and the constraint condition two, d can be takenl＝dr＝283.887，dz＝133.5。
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict. Although the present invention has been described to a certain extent, it is apparent that appropriate changes in the respective conditions may be made without departing from the spirit and scope of the present invention. It is to be understood that the invention is not limited to the described embodiments, but is to be accorded the scope consistent with the claims, including equivalents of each element described.

Claims (2)

1. A method for determining a curved flight segment comprises the following steps:
s1, establishing a flight path curve model;
s2, regression simulating the flight segment based on the flight segment curve model;
s3 estimating the flight segment lateral flight error distribution of the regression simulation;
s4 estimating a vertical flight error distribution for the regression-modeled leg,
wherein, the S1 establishes a flight segment curve model, including:
flight segment curve l(s) ═ x(s), y (s)), including length l0Straight line of radius r1Central angle of alpha1Arc of (d) with radius r2Central angle of alpha2Arc of (d), slope k ═ tan (α)1-α2) A straight line of (a);
the mathematical expression of l(s) ═ x(s), y (s)) is:
Figure FDA0002784889580000011
Figure FDA0002784889580000012
wherein l0＝x0，l1＝x0+r1α1，l2＝x0+r1α1+r2α2，
x2＝x0+r1sinα1+r2(sinα1-sin(α1-α2))
y2＝y0+r1(1-cosα1)-r2(cosα1-cos(α1-α2))
L(s) is defined by the parameter (x)0，y0，r1，α1，r2，α2) Is uniquely determined, wherein the length is l0Has an end point of (x)0，y0)；
The S3 estimating a leg lateral flight error distribution, including:
s301, taking the step length as delta S, and dividing the flight segment curve into sub-flight segments Li＝L(s)，s∈[i×Δs，(i+1)×Δs]Assume each sub-flight segment LiLateral flight error epsilon corresponding to each point in the aircrafty(s) all satisfy a standard deviation of σiNormal distribution of (i), i.e. for any s e [ i x Δ s, (i +1) x Δ s]，εy(s)～N(0，σi) Where σ isiIs the standard deviation;
the normal plane nplane (S) of the curve of the flight segment of S302 is:
Figure FDA0002784889580000013
Figure FDA0002784889580000021
is a vertical unit vector of the unit,
Figure FDA0002784889580000022
normal vector for curve L(s);
using sample points between nplane (i × Δ s) and nplane ((i +1) × Δ s), poles were takenObtaining a parameter sigma by a large likelihood estimation methodiThe parameter estimation value of (2);
s303 compares the parameter sigmaiIs introduced into epsilony(s)～N(0，σi) Obtaining the lateral flight error epsilon of the flight segment L(s)y(s) a distribution function;
the S4 estimating a vertical flight error distribution of the leg, including:
s401 for a given S, the actual position of the flight z (S) should be predicted from zintend(s) and systematic flight errors by aircraft
Figure FDA0002784889580000023
Composition is carried out;
assuming aircraft system errors
Figure FDA0002784889580000024
Predicted position zintend(s) obey a uniform distribution over a certain interval, i.e.: z is a radical ofintend(s)～U[z1(s)，z2(s)](ii) a Get zintend(s) the median line generated is the leg, then the vertical flight error due to uncertainty in the predicted trajectory
Figure FDA0002784889580000025
Satisfies the distribution U < -z [ ]0(s)，z0(s)]Suppose that
Figure FDA0002784889580000026
And system flight error
Figure FDA00027848895800000213
Independent of each other, then random vectors
Figure FDA0002784889580000027
Has a joint probability density function of
Figure FDA0002784889580000028
So epsilonz(s) a probability density function p (x) of:
Figure FDA0002784889580000029
wherein the function erf (x) is referred to as the error function of x, defined as:
Figure FDA00027848895800000210
s402 for each segment LiUsing sample point drive-in (6) between nplane (i × Δ s) and nplane ((i +1) × Δ s), sample data adopts maximum likelihood estimation method to estimate parameters
Figure FDA00027848895800000211
S403, parameter
Figure FDA00027848895800000212
The parameter estimation value belt (6) obtains the vertical flight error epsilon of the flight section L(s)zProbability density function p (x) of(s).
2. The method of claim 1, wherein the S2 regression modeling a leg, comprising:
s201 note diIs a sample point (X)i，Yi) The distance to the flight profile l(s), i.e.:
Figure FDA0002784889580000031
where inf represents the infimum bound of the set of real numbers
S202, optimizing an objective function LS (x) by using a least square method0，y0，r1，α1，r2，α2)，
Figure FDA0002784889580000032
The obtained parameter (x)0，y0，r1，α1，r2，α2) Best fit parameters for the flight profile l(s);
s203, the best fitting parameters are brought into the formula (1) and the formula (2), and a mathematical expression of L (S) is obtained.
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