A method for fitting and displaying aircraft turning trajectories based on Euler spirals

Abstract

This invention discloses a method for fitting and displaying aircraft turning trajectories based on the Euler spiral. The method uses the Euler spiral as a transition between straight lines and circular arcs, dividing the aircraft turning trajectory into five parts: straight line - Euler spiral - circular arc - Euler spiral - straight line. It combines optimization methods to optimize parameters, achieving accurate fitting of the aircraft's turning trajectory. Specifically, it includes: designing an aircraft turning trajectory fitting curve based on the straight line - Euler spiral - circular arc - Euler spiral - straight line approach; designing an experience-based fitting parameter initialization method; designing a turning trajectory loss function based on mean square error; and designing a parameter optimization method based on a genetic algorithm. This method optimizes current schemes that use polylines or circular arcs for aircraft turning trajectory fitting, and is helpful for subsequent work on digital twins, metaverse, etc.

Description

Technical Field

[0001] This invention relates to a method for fitting and displaying aircraft turning trajectories, and more particularly to a method for fitting and displaying aircraft turning trajectories based on Euler spirals. Background Technology

[0002] In current simulation systems and various charts, aircraft turning trajectories are mostly represented by broken lines or arcs. However, modern applications place increasingly higher demands on aircraft trajectory description, and broken lines and arcs are becoming insufficient. For example, in existing aircraft trajectory simulation systems (such as 4D flight path air traffic control simulation systems), using only broken lines and arcs to describe aircraft trajectories results in significant deviations from actual trajectories and requires additional manual correction steps.

[0003] A few researchers have explored using other arcs instead of broken lines and circular arcs to describe aircraft turning trajectories; however, the descriptions are either not accurate enough or lack complete parameter estimation methods.

[0004] Therefore, there is an urgent need for a relatively accurate method for fitting aircraft turning trajectories. The fitting results of this method should be describable by parameters, and these parameters should be obtainable through certain calculations, and should not be NP hard problems (NP, non-deterministic polynomial, refers to problems that can be reduced to polynomial time complexity). Summary of the Invention

[0005] Purpose of the invention: The technical problem to be solved by the present invention is to provide a method for fitting and displaying aircraft turning trajectories based on Euler spirals, which addresses the shortcomings of existing technologies.

[0006] To address the aforementioned technical problems, this invention discloses a method for fitting and displaying aircraft turning trajectories based on the Euler spiral, comprising the following steps:

[0007] Step 1, Model Building: This involves building a curve consisting of five parts: a first straight line, a first Euler spiral, a circular arc, a second Euler spiral, and a second straight line, which is used to fit the aircraft turning point data.

[0008] The curve, i.e., the aircraft turning trajectory, consists of five parts: a first straight line, a first Euler spiral, a circular arc, a second Euler spiral, and a second straight line. These correspond to the aircraft turning point data sorted by time from the beginning to the end: FP0, FP1, ..., FP N-1， FP N Where FP0 is the origin, i.e., the entry point of the curve, and FP... N The endpoint is the exit point, and N is the number of turning points.

[0009] Step 2: Design parameters and constraints for each of the five parts of the curve in the model, so that the curve drawn by the five parts is continuous and the derivative is continuous.

[0010] The design parameters include:

[0011] The first straight line is represented by its direction θ1 and length s1;

[0012] The first Euler spiral is represented by the scaling factor A1, R1 is the radius of curvature at the beginning, R2 is the radius of curvature at the end, t1 is the length of the first Euler spiral from the origin, and s2 represents the length.

[0013] The radius of curvature of an arc is represented by r3, and the length is represented by s3;

[0014] The second Euler spiral is represented by A2 as the scaling factor, R4 as the radius of curvature at the beginning, and s4 as the length.

[0015] The second straight line is represented by its direction θ5 and length s5.

[0016] The design constraints include:

[0017] The end of the first straight line is continuous with the beginning of the first Euler spiral, and at the beginning of the first Euler spiral, t1 = 0 and the radius of curvature R1 is infinite, thus ensuring that the end of the first straight line is continuous with the beginning of the first Euler spiral and that the derivative is continuous.

[0018] The end of the first Euler spiral and the beginning of the arc are continuous, and the radius of curvature R2 at the end of the first Euler spiral is equal to the radius r of the arc, thus ensuring that the first Euler spiral and the arc are continuous and the derivative is continuous.

[0019] The end of the circular arc is continuous with the beginning of the second Euler spiral, and the radius of curvature R4 at the beginning of the Euler spiral is equal to the radius r of the circular arc, thus ensuring that the second Euler spiral and the circular arc are continuous and the derivative is continuous.

[0020] The end of the second Euler spiral is continuous with the beginning of the second straight line, and its derivative is continuous.

[0021] Step 3: Design a parameter initialization method based on historical experience to calculate the initial values ​​of the parameters in the model, specifically including:

[0022] Step 3-1: Construct a sliding window of length n1 for the aircraft turning point data. The sliding window starts from the earliest point in time, i.e., the origin FP0, and moves backward. Within each window, connect the start and end points in time to obtain the direction of motion θ of the point data within the window. i Compare θ0 in the earliest window in time sequence with θ in the current sliding window. iWhen the difference is greater than the threshold Δθ, the initial point of the current sliding window is taken as the initial point P of the aircraft's turn. 1-2 Calculate the initial point to point P of the aircraft track data. 1-2 The distance is taken as s1;

[0023] Step 3-2, connect point FP0 and point P from step 3-1. 1-2 A line segment is obtained, and the direction of this line segment is taken as the initial value θ1 of the aircraft's entry angle into the curve;

[0024] Step 3-3: Construct a sliding window of length n2 for the aircraft turning point data. The sliding window starts from the latest point in time, i.e., the endpoint FP. N Start moving forward, and perform linear fitting on the aircraft spot data within each window to obtain the motion direction θ of the spot data within the window. i Compare θ in the latest window in the time sequence N and θ in the current sliding window i When the difference is greater than the threshold Δθ, the last point of the current sliding window is taken as the initial point P for the aircraft's direct flight. 4-5 Calculate the distance from the end point of the aircraft track data to point P. 4-5 The distance is taken as s5;

[0025] Steps 3-4: Transfer the distance from point FP0 to point P. 1-2 The extension line and point FP N Point P 4-5 The extensions of the two lines are given, and the intersection of the two extensions is X. Calculate point P. 1-2 Let s'1 be the distance from point X to point P. Calculate the distance from point X to point P. 4-5 The distance is denoted as s'2. For the angle θ′ between the line segments at the intersection point X, the line segments are divided into 18 turning categories at 10-degree intervals. A proportional coefficient λ is designed as an empirical parameter for each category, and the initial values ​​of s2, s3, and s4 are calculated. The specific method is as follows:

[0026] s2=λ 1-2 s′1+λ 2-2 s′2

[0027] s3=λ 1-3 s′1+λ 2-3 s′2

[0028] s4=λ 1-4 s′1+λ 2-4 s′2

[0029] Where, λ 1-2 λ represents the correlation coefficient between s′1 and s2. 2-2 λ represents the correlation coefficient between s′2 and s2. 1-3 λ represents the correlation coefficient between s′1 and s3.2-3 λ represents the correlation coefficient between s′2 and s3. 1-4 λ represents the correlation coefficient between s′1 and s4. 2-4 This represents the correlation coefficient between s′2 and s4.

[0030] Step 4: Design a loss function to describe the error between the current fitted curve and the real aircraft spot, providing guidance for parameter optimization in the model;

[0031] The design loss function specifically includes:

[0032] Step 4-1: Starting from the earliest track point FP0 in time sequence, calculate the distances from FP0 to the first straight line and the first Euler spiral respectively, and take the smaller of the two values ​​as the distance from point FP0 to the fitted curve.

[0033] Step 4-2: Among the subsequent track points in chronological order, find the track point FP that begins to enter the descriptive range of the first Euler spiral. n The specific method is as follows:

[0034] Following the chronological order, subsequent path points FP1, FP2, ... are taken. The distance from each subsequent path point to the first straight line and the first Euler spiral is calculated, and the smaller of the two values ​​is taken as the distance from each subsequent path point to the fitted curve. This process continues until the nth path point FP... n From FP n-4 To FP n If the distances from these five points to the first Euler spiral are all less than the distances to the first straight line, then they are considered as the current track point FP. n It has already entered the scope of the description of the first Euler spiral.

[0035] Step 4-3, from point FP n Begin by calculating FP. n The smaller of the distances to the first Euler spiral and the circular arc is taken as the point FP. n Distance to the fitted curve;

[0036] Step 4-4: Among the subsequent trackpoints in chronological order, find the trackpoint FP that begins to enter the described range of the arc. n+m Specific methods include:

[0037] Collect subsequent trackpoints (FP) in chronological order. n+1 FP n+2 …Calculate the distance from each subsequent track point to the first Euler spiral and the circular arc, and take the smaller of the two as the distance from each subsequent track point to the fitted curve, until the (n+m)th track point FP… n+m From FP n+m-4 To FP n+mIf the distances from these five points to the circular arcs are all less than the distances to the first Euler spiral, then they are considered as the current track point FP. n+m It has now fallen within the scope of the description of an arc.

[0038] Step 4-5: Using the methods from Step 4-1 to Step 4-4, find the range of track points for the second Euler spiral and the second straight line;

[0039] Steps 4-6: After obtaining the range of the real track points corresponding to all 5 parts, calculate the distance from each track point to the fitted curve, and take the mean squared error as the loss function from the current fitted curve to the real track point.

[0040] Step 5: Design parameter optimization methods to minimize the loss function, achieve common optimization of the five parts of the curve in the model, and complete the fitting of the aircraft turning point data, that is, complete the fitting of the aircraft turning trajectory based on the Euler spiral.

[0041] The parameters specifically include:

[0042] The direction of the first straight line (angle θ1), the length of the first straight line (s1), the scaling factor A1 of the first Euler spiral, the length of the first Euler spiral (s2), the length of the arc (s3), the length of the second Euler spiral (s4), and the length of the second straight line (s5) are selected as the seven parameters describing the fitted curve.

[0043] The aforementioned design parameter optimization method specifically includes:

[0044] Step 5-1: Use the initial values ​​of the six parameters θ1, s1, s2, s3, s4, and s5 determined in Step 3, and randomly generate XX sets of parameters A1 to obtain XX sets of initial parameter values ​​consisting of 7 parameters.

[0045] Step 5-2: Use a genetic algorithm to iterate from the initial parameter values ​​of XX groups. For the fitting curve consisting of 7 parameters in each iteration, calculate the loss function from the real track to the fitting curve according to the method in step 4. Select the XX1 fitting curves with the smallest loss function, pair them up, take the mean of the 7 parameters in each pair, and add a random perturbation within a set range to generate the first generation.

[0046] Step 5-4: Calculate the loss function for each fitted curve in the first generation, take the XX2 curves with the smallest loss function and pair them to form the second generation. Repeat the above steps until the variance of the loss function of the current generation is less than the set threshold Δ.

[0047] Step 5-5: Take the fitted curve with the smallest loss function in the current offspring as the fitting result for the real turning trajectory data.

[0048] Steps 5-6 record the parameters s'1, s'2, θ′, s2, s3, and s4 of the fitted curve finally selected in Step 5-5, and use them to calculate and update the scaling factor λ value in Step 3-4.

[0049] Step 6: Based on the above method, the aircraft's turning trajectory is directly calculated from the original trajectory data measured by the aircraft, and then displayed in the existing aircraft trajectory simulation system.

[0050] Beneficial effects:

[0051] It can accurately describe the turning trajectory of an aircraft, and the fitting results can be directly calculated from the original trajectory data without any additional manual steps. Attached Figure Description

[0052] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and / or other aspects will become clearer.

[0053] Figure 1 This is a schematic diagram of an aircraft turning trajectory fitting and display method based on the Euler spiral.

[0054] Figure 2 This is a flowchart of parameter estimation for an aircraft turning trajectory fitting and display method based on the Euler spiral.

[0055] Figure 3 This is a schematic diagram illustrating the estimation method for s1 and s5 in the fitted curve.

[0056] Figure 4 This is a schematic diagram showing the relevant positions of each point in the fitted curve.

[0057] Figure 5 This is a flowchart of a method for optimizing parameters related to a fitted curve based on a genetic algorithm. Detailed Implementation

[0058] The principle of this invention is to describe the aircraft turning trajectory using a straight line-Euler spiral-circular arc-Euler spiral-straight line method, and to obtain the parameter values ​​of the fitted curve by minimizing the variance between the fitted curve and the actual track point using a genetic algorithm.

[0059] A method for fitting and displaying aircraft turning trajectories based on the Euler spiral includes the following steps:

[0060] Step 1: Create a curve consisting of five parts: straight line, Euler spiral, circular arc, Euler spiral, and straight line, to fit the aircraft turning point data;

[0061] Step 2: Design parameters and constraints for each of the five parts of the model to ensure that the curve plotted by the five parts is continuous and the derivative is continuous.

[0062] Step 3: Design a parameter initialization method based on historical experience to provide an initial value for the model parameters, which facilitates the implementation of subsequent optimization methods and avoids convergence to local optima;

[0063] Step 4: Design a loss function to describe the error between the current fitted curve and the real aircraft spot, thereby providing guidance for parameter optimization;

[0064] Step 5: Design parameter optimization methods to minimize the loss function and achieve joint optimization of five parts: straight line, Euler spiral, circular arc, Euler spiral, and straight line, to complete the fitting of aircraft turning point data.

[0065] Step 6: Based on the above method, the aircraft's turning trajectory is directly calculated from the original trajectory data measured by the aircraft, and then displayed in the existing aircraft trajectory simulation system.

[0066] Furthermore, step 2 includes:

[0067] Step 2-1: The trajectory is divided into 5 parts: straight line 1, Euler spiral 1, circular arc, Euler spiral 2, and straight line 2. These correspond to the aircraft turning point data sorted by time from the beginning to the end (FP0, FP1, ..., FP...). N-1， FP N ), with FP0 as the origin;

[0068] Step 2-2: Line 1 is represented by direction θ1 and length s1; Euler spiral 1 is represented by the scaling factor A1 (the expression for the Euler spiral is A...). 2 =R*t, where R is the radius of curvature, t is the length of the spiral from the origin, A is the scaling factor, and s2 represents the length; the radius of curvature of the arc is represented by r3, and the length by s3; the scaling factor of the Euler spiral is represented by A2, and the length by s4; the straight line is represented by the direction θ5 and the length s5.

[0069] Steps 2-3: The end of line 1 is continuous with the beginning of Euler spiral 1, and at the beginning of Euler spiral 1, t=0, the radius of curvature R is infinite, thus ensuring that the end of line 1 is continuous with the beginning of Euler spiral 1 and the derivative is continuous.

[0070] Step 2-4: The end of Euler spiral 1 and the beginning of the arc are continuous, and the radius of curvature R2 at the end of Euler spiral 1 is equal to the radius r of the arc, thus ensuring that Euler spiral 1 and the arc are continuous and the derivative is continuous.

[0071] Steps 2-5: The end of the circular arc is continuous with the beginning of the Euler spiral 2, and the radius of curvature R4 at the beginning of the Euler spiral is equal to the radius r of the circular arc, thus ensuring that the Euler spiral 2 and the circular arc are continuous and the derivative is continuous.

[0072] Steps 2-6: The end of Euler spiral 2 is continuous with the beginning of line 2 and its derivative is continuous;

[0073] Furthermore, step 3 includes:

[0074] Step 3-1: Construct a sliding window of length n1 for the aircraft turning track data. The size of n1 can be determined according to the density of track points in the time series. The sliding window moves backward from the earliest track FP0 in the time series. Within each window, connect the start point and the end point in the time series to obtain the motion direction θ of the track data within the window. i Compare θ0 in the earliest window in time sequence with θ in the current sliding window. i When the difference is greater than the threshold Δθ, the initial point of the current sliding window is taken as the initial point P of the aircraft's turn. 1-2 Calculate the distance from the initial point of the aircraft track data to this point as s1;

[0075] Step 3-2, connect FP0 and P in step 3-1 1-2 The direction of this line segment is taken as the initial value θ1 of the aircraft's entry angle into the curve;

[0076] Step 3-3: Construct a sliding window of length n2 for the aircraft turn track data. The size of n2 depends on the temporal density of the track points. The sliding window starts from the latest track FP in the temporal sequence. N Start moving forward, and perform linear fitting on the aircraft spot data within each window to obtain the motion direction θ of the spot data within the window. i Compare θ in the latest window in the time sequence N and θ in the current sliding window i When the difference is greater than the threshold Δθ, the last point of the current sliding window is taken as the initial point P for the aircraft's direct flight. 4-5 Calculate the distance from the last point of the aircraft track data to this point as s5;

[0077] Steps 3-4: Perform FP0 to P 1-2 extensions and FP N To P 4-5 The extensions of the two lines are given, and the intersection point of the two lines is X. Calculate P. 1-2 Let s'1 be the distance from X to P. Calculate the distance from X to P. 4-5 The distance is denoted as s'2, and the specific positional relationship is shown in [reference needed]. Figure 4 Divide the line segments at the intersection point into 18 turning categories at 10-degree intervals, and design a proportional coefficient λ as an empirical parameter for each category. Calculate the initial values ​​of s2, s3, and s4 according to the following formula;

[0078] s2=λ 1-2 s′1+λ2-2 s′2

[0079] s3=λ 1-3 s′1+λ 2-3 s′2

[0080] s4=λ 1-4 s′1+λ 2-4 s′2

[0081] Furthermore, step 4 includes:

[0082] Step 4-1: Starting from the earliest track point FP0 in time sequence, calculate the distances from FP0 to line 1 and Euler spiral 1 respectively, and take the relatively smaller value as the distance from FP0 to the fitted curve.

[0083] Step 4-2: Take subsequent waypoints FP1, FP2, ... in chronological order, and calculate the distance from FP to line 1 and Euler spiral 1 respectively. Take the relatively smaller value as the distance from FP to the fitted curve, until a certain waypoint FP... n From FP n-4 To FP n If the distance from these five points to Euler spiral 1 is less than the distance to straight line 1, then they are considered as the current track point FP. n This has already fallen within the scope of the description of Euler spiral 1;

[0084] Step 4-3, from FP n Begin by calculating FP. n The distance to Euler spiral 1 and the arc is taken as the relatively smaller value as FP. n Distance to the fitted curve;

[0085] Step 4-4: Obtain subsequent waypoints (FP) in chronological order. n+1 FP n+2 …The distances from FP to the Euler spiral 1 and the circular arc are calculated separately, and the smaller value is taken as the distance from FP to the fitted curve, until FP reaches a certain track point. n+m From FP n+m -4 to FP n+m If the distance from these five points to the arc is less than the distance to Euler spiral 1, then the current track point is considered to have entered the description range of the arc.

[0086] Steps 4-5: Using a method similar to steps 4-1 to 4-4, find the range of track points for Euler spiral 2 and straight line 2;

[0087] Steps 4-6: After obtaining the range of the real track points corresponding to all 5 line segments, calculate the distance from each track point to the fitted curve, and take the mean squared error as the loss function from the current fitted curve to the real track point.

[0088] Furthermore, step 5 includes:

[0089] Step 5-1: Taking FP0 as the origin, a complete turning curve can be drawn based on the angle θ1 and length s1 of line 1, the length s2 and scale factor A1 of Euler spiral 1, the length s3 of the arc, the length s4 and scale factor A2 of Euler spiral 2, and the angle θ2 and length s5 of line 2. Since θ1 and θ2 influence each other, only one needs to be retained due to the influence of continuous derivatives. Therefore, only three parameters among A1, s2, A2, and s4 are needed to uniquely determine the coordinates of the two Euler spirals. In this invention, we select θ1, s1, A1, s2, s3, s4, and s5 as all seven parameters describing the fitted curve;

[0090] Step 5-2: Using the initial values ​​of the six parameters θ1, s1, s2, s3, s4, and s5 determined in Step 3, 10,000 sets of A1 are randomly generated to obtain 10,000 sets of initial parameter values ​​consisting of 7 parameters.

[0091] Step 5-3: Use a genetic algorithm to iterate from 10,000 initial values. For each iteration, the fitting curve consisting of 7 parameters is calculated according to step 4 to obtain the loss function from the real track to the fitting curve. Select the 100 fitting curves with the smallest loss function, pair them up, take the mean of the 7 parameters in each pair, and add a random perturbation within plus or minus 5% to generate the first generation.

[0092] Step 5-4: Calculate the loss function for each fitted curve in the first generation, take the 100 smallest ones and combine them in pairs to form the second generation, and so on, until the variance of the loss function of the current generation is less than a certain threshold Δ.

[0093] Step 5-5: Take the fitted curve with the smallest loss function in the current offspring as the fitting result for the real turning trajectory data.

[0094] Steps 5-6 record s'1, s'2, θ′, s2, and s3 of the finally selected fitted curve, and use them to calculate and update the scaling factor λ value in step 3-4.

[0095] Example:

[0096] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described below with reference to the accompanying drawings and embodiments. Since the description of the embodiments is specific and cannot cover all embodiments of this invention, all other embodiments obtained by those skilled in the art without innovative effort are within the protection scope of this invention.

[0097] like Figure 1 The diagram shows a method for fitting and displaying aircraft turning trajectories based on the Euler spiral. This method divides the aircraft's turning process into five parts: straight line, Euler spiral, circular arc, Euler spiral, and straight line. The straight line represents the part where the aircraft flies normally in a straight line, the Euler spiral represents the part where the turning radius changes continuously during the aircraft's entry and exit from the turn, and the circular arc represents the part where the aircraft turns and flies stably at a certain angle.

[0098] The aircraft turning trajectory fitted by the method of this invention can be loaded into a 4D flight path air traffic control simulation system to further enhance the accuracy of the aircraft turning trajectory in the aircraft simulation system, thereby better simulating the actual aircraft flight trajectory.

[0099] like Figure 2 The diagram shows the parameter estimation flowchart for an aircraft turning trajectory fitting method based on the Euler spiral. It describes the calculation process of seven variables—θ1, s1, A1, s2, s3, s4, and s5—in the aircraft turning trajectory fitting process. These seven variables are, respectively, the aircraft's entry angle, the length of the straight line in the entry segment, the scaling factor of the Euler spiral in the entry segment, the length of the Euler spiral in the entry segment, the arc length, the length of the Euler spiral in the exit segment, and the straight line length in the exit segment. These seven variables can uniquely determine an aircraft turning trajectory fitting curve composed of a straight line, an Euler spiral, an arc, an Euler spiral, and a straight line. The premise of parameter estimation is that the second derivative is continuous at the intersection points between each line segment.

[0100] like Figure 3 The diagram illustrates the estimation method for s1 and s5 in the fitted curve. The sliding window starts at FP0 and slides sequentially forward. The window length n1 is set to 6 here, but can be modified according to actual needs. Within each sliding window, the earliest and latest time-series track points are connected, and the direction of the resulting line segment is marked as θ. i The direction of the sliding window starting at FP0 is marked as θ0, P 1-2 For θ i For the track point where -θ0 first exceeds the threshold Δθ, the distance to FP0 is an estimate of s1, and the distance from FP0 to P... 1-2 The direction of the line segment is the aircraft's entry angle θ1. The estimation of s5 is similar to that of s1, except that it needs to be slid forward from the last sliding window in the time sequence.

[0101] like Figure 4The diagram shows the relative positions of points on the fitted curve. θ' represents the angle between the entry and exit angles, which largely determines the aircraft's turning pattern. This angle is divided into 18 turning types at 10-degree intervals, and a scaling factor λ is constructed for each type for parameter estimation of s2, s3, and s4. The angle in the diagram is approximately 75 degrees, falling within the 70-80 degree range; therefore, the scaling factor λ within this range is needed for parameter estimation. Similar ranges include 0-10 degrees, 30-40 degrees, 90-100 degrees, and 170-180 degrees, etc., and the scaling factor λ for each range needs to be calculated and statistically analyzed separately.

[0102] like Figure 5 The diagram shows the flowchart of the parameter optimization method for fitting curves based on a genetic algorithm. In the initialization part, the six parameters θ1, s1, s2, s3, s4, and s5 (excluding A1) are given by the parameter initialization method in step 3. A1 takes the maximum and minimum values ​​from the experimental data, using a uniform distribution to select values ​​from this interval. When the 100 sets of parameters in the parent generation of the genetic algorithm are combined pairwise, the parent data is retained, so the offspring generation still has 10,000 sets of parameters. The loss function threshold Δ can be determined according to the requirements; a smaller threshold can be set if a more accurate fitting curve is required, while a relatively larger threshold can be set if accuracy requirements are not high.

[0103] Based on the above method, the aircraft's turning trajectory is directly calculated from the original trajectory data measured by the aircraft, fitted, and displayed in the existing aircraft trajectory simulation system.

[0104] In its specific implementation, this application provides a computer storage medium and a corresponding data processing unit. The computer storage medium is capable of storing a computer program, which, when executed by the data processing unit, can run the invention's content regarding an aircraft turning trajectory fitting and display method based on the Euler spiral, as well as some or all of the steps in various embodiments. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0105] Those skilled in the art will clearly understand that the technical solutions in the embodiments of the present invention can be implemented using computer programs and their corresponding general-purpose hardware platforms. Based on this understanding, the technical solutions in the embodiments of the present invention, or the parts that contribute to the prior art, can be embodied in the form of computer programs, i.e., software products. These computer program software products can be stored in a storage medium and include several instructions to cause a device containing a data processing unit (which may be a personal computer, server, microcontroller, MUU, or network device, etc.) to execute the methods described in various embodiments or certain parts of the embodiments of the present invention.

[0106] This invention provides a method and approach for fitting and displaying aircraft turning trajectories based on the Euler spiral. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A method for fitting and displaying aircraft turning trajectories based on the Euler spiral, characterized in that, Includes the following steps: Step 1, Model Building: This involves building a curve consisting of five parts: a first straight line, a first Euler spiral, a circular arc, a second Euler spiral, and a second straight line, which is used to fit the aircraft turning point data. Step 2: Design parameters and constraints for each of the five parts of the curve in the model, so that the curve drawn by the five parts is continuous and the derivative is continuous. Step 3: Design a parameter initialization method based on historical experience and calculate the initial values ​​of the parameters in the model; Step 4: Design a loss function to describe the error between the current fitted curve and the real aircraft spot, providing guidance for parameter optimization in the model; Step 5: Design parameter optimization methods to minimize the loss function, achieve common optimization of the five parts of the curve in the model, and complete the fitting of the aircraft turning point data, that is, complete the fitting of the aircraft turning trajectory based on the Euler spiral. Step 6: Based on the above method, the aircraft's turning trajectory is directly calculated from the original trajectory data measured by the aircraft, and then displayed in the existing aircraft trajectory simulation system. The curve described in step 1, i.e. the aircraft turning trajectory, comprises 5 parts, respectively: a first straight line, a first Euler spiral, a circular arc, a second Euler spiral, a second straight line, corresponding to the initial to the end of the aircraft turning point trajectory data ordered by time: FP0, FP1, …, FP N-1， FP N , wherein FP0 is the origin, i.e. the entry point, FP N is the end point, i.e. the exit point, and N is the number of turning points; The design parameters mentioned in step 2 include: The first straight line uses direction It is represented by the length s1; The first Euler spiral is represented by the scaling factor A1, R1 is the radius of curvature at the beginning, R2 is the radius of curvature at the end, t1 is the length of the first Euler spiral from the origin, and s2 represents the length. The radius of curvature of an arc is represented by r3, and the length is represented by s3; The second Euler spiral is represented by A2 as the scaling factor, R4 as the radius of curvature at the beginning, and s4 as the length. The second straight line uses direction. And the length s5 is used to represent it; The initial values ​​of the parameters in the computational model described in step 3 specifically include: Step 3-1: Construct a sliding window of length n1 for the aircraft turning point data. The sliding window starts from the earliest point in time, i.e., the origin FP0, and moves backward. Within each window, connect the start and end points in time to obtain the direction of movement of the point data within the window. Compare the earliest window in the time sequence And in the current sliding window The difference, when greater than the threshold At that time, the initial point of the current sliding window is taken as the initial point P of the aircraft's turn. 1-2 Calculate the initial point to point P of the aircraft track data. 1-2 The distance is taken as s1; Step 3-2, connect point FP0 and point P from step 3-1. 1-2 This yields a line segment, the direction of which is taken as the initial value of the aircraft's entry angle into the curve. ; Step 3-3: Construct a sliding window of length n2 for the aircraft turning point data. The sliding window starts from the latest point in time, i.e., the endpoint FP. N Start moving forward, and perform linear fitting on the aircraft spot data within each window to obtain the direction of movement of the spot data within the window. Compare the latest window in the time sequence And in the current sliding window The difference, when greater than the threshold At that time, the last point of the current sliding window is taken as the initial point P for the aircraft's straight flight. 4-5 Calculate the distance from the end point of the aircraft track data to point P. 4-5 The distance is taken as s5; Steps 3-4: Transfer the distance from point FP0 to point P. 1-2 The extension line and point FP N Point P 4-5 The extensions of the two lines are given, and the intersection of the two extensions is X. Calculate point P. 1-2 The distance to point X is denoted as Calculate the distance from point X to point P. 4-5 The distance is denoted as For the angle between the line segments at intersection point X The turns are divided into 18 categories at 10-degree intervals. A proportional coefficient λ is designed as an empirical parameter for each category, and the initial values ​​of s2, s3, and s4 are calculated. The specific method is as follows: ； in, Indicate The correlation coefficient with s2, express The correlation coefficient with s2, express The correlation coefficient with s3, express The correlation coefficient with s3, express Correlation coefficient with s4 Indicate Correlation coefficient with s4.

2. The method for fitting and displaying aircraft turning trajectories based on the Euler spiral according to claim 1, characterized in that, The design constraints mentioned in step 2 include: The end of the first straight line is continuous with the beginning of the first Euler spiral, and at the beginning of the first Euler spiral, t1=0 and the radius of curvature R1 is infinite, thus ensuring that the end of the first straight line is continuous with the beginning of the first Euler spiral and that the derivative is continuous. The end of the first Euler spiral and the beginning of the arc are continuous, and the radius of curvature R2 at the end of the first Euler spiral is equal to the radius r of the arc, thus ensuring that the first Euler spiral and the arc are continuous and the derivative is continuous. The end of the circular arc is continuous with the beginning of the second Euler spiral, and the radius of curvature R4 at the beginning of the Euler spiral is equal to the radius r of the circular arc, thus ensuring that the second Euler spiral and the circular arc are continuous and the derivative is continuous. The end of the second Euler spiral is continuous with the beginning of the second straight line, and its derivative is continuous.

3. The method for fitting and displaying aircraft turning trajectories based on the Euler spiral according to claim 2, characterized in that, The design loss function mentioned in step 4 specifically includes: Step 4-1: Starting from the earliest track point FP0 in time sequence, calculate the distances from FP0 to the first straight line and the first Euler spiral respectively, and take the smaller of the two values ​​as the distance from point FP0 to the fitted curve. Step 4-2: Among the subsequent track points in chronological order, find the track point FP that begins to enter the descriptive range of the first Euler spiral. n ; Step 4-3, from point FP n Begin by calculating FP. n The smaller of the distances to the first Euler spiral and the circular arc is taken as the point FP. n Distance to the fitted curve; Step 4-4: Among the subsequent trackpoints in chronological order, find the trackpoint FP that begins to enter the described range of the arc. n+m ; Step 4-5: Using the methods from Step 4-1 to Step 4-4, find the range of track points for the second Euler spiral and the second straight line; Steps 4-6: After obtaining the range of the real track points corresponding to all 5 parts, calculate the distance from each track point to the fitted curve, and take the mean squared error as the loss function from the current fitted curve to the real track point.

4. The method for fitting and displaying aircraft turning trajectories based on the Euler spiral according to claim 3, characterized in that, Step 4-2 describes finding the track point FP, which marks the beginning of the description range of the first Euler spiral. n The specific method is as follows: Following the chronological order, subsequent path points FP1, FP2, ... are taken. The distance from each subsequent path point to the first straight line and the first Euler spiral is calculated, and the smaller of the two values ​​is taken as the distance from each subsequent path point to the fitted curve. This process continues until the nth path point FP... n From FP n-4 To FP n If the distances from these five points to the first Euler spiral are all less than the distances to the first straight line, then they are considered as the current track point FP. n It has already entered the scope of the description of the first Euler spiral.

5. The method for fitting and displaying aircraft turning trajectories based on the Euler spiral according to claim 4, characterized in that, Step 4-4 describes finding the track point FP that begins to enter the described range of the circular arc. n+m Specific methods include: Collect subsequent trackpoints (FP) in chronological order. n+1 FP n+2 …Calculate the distance from each subsequent track point to the first Euler spiral and the circular arc, and take the smaller of the two as the distance from each subsequent track point to the fitted curve, until the (n+m)th track point FP… n+m From FP n+m-4 To FP n+m If the distances from these five points to the circular arcs are all less than the distances to the first Euler spiral, then they are considered as the current track point FP. n+m It has now fallen within the scope of the description of an arc.

6. The method for fitting and displaying aircraft turning trajectories based on the Euler spiral according to claim 5, characterized in that, The parameters mentioned in step 5 specifically include: Choose the direction, i.e., the angle, of the first straight line. The lengths of the first straight line (s1), the scaling factor A1 of the first Euler spiral, the lengths of the first Euler spiral (s2), the lengths of the arc (s3), the lengths of the second Euler spiral (s4), and the lengths of the second straight line (s5) are the seven parameters describing the fitted curve.

7. The method for fitting and displaying aircraft turning trajectories based on the Euler spiral according to claim 6, characterized in that, The design parameter optimization method described in step 5 specifically includes: Step 5-1, using the method determined in step 3. The initial values ​​of six parameters s1, s2, s3, s4, and s5 are determined, and XX sets of parameters A1 are randomly generated to obtain XX sets of initial parameter values ​​consisting of 7 parameters. Step 5-2: Use a genetic algorithm to iterate from the initial parameter values ​​of XX groups. For the fitting curve consisting of 7 parameters in each iteration, calculate the loss function from the real track to the fitting curve according to the method in step 4. Select the XX1 fitting curves with the smallest loss function, pair them up, take the mean of the 7 parameters in each pair, and add a random perturbation within a set range to generate the first generation. Step 5-4: Calculate the loss function for each fitted curve in the first generation, take the XX2 curves with the smallest loss function and pair them to form the second generation. Repeat the above steps until the variance of the loss function of the current generation is less than the set threshold Δ. Step 5-5: Take the fitted curve with the smallest loss function in the current offspring as the fitting result for the real turning trajectory data. Steps 5-6 involve refining the parameters of the final fitted curve selected in step 5-5. , , S1, S2, S3, and S4 are recorded and used to calculate and update the scaling factor λ value in steps 3-4.

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