A trajectory smoothing system and method based on ADS-B dynamics constraints

Abstract

The application belongs to the technical field of aircraft monitoring and trajectory processing, and particularly relates to a trajectory smoothing system and method based on ADS-B dynamic constraint, which comprises the following steps: performing coordinate conversion on original ADS-B data; analyzing an ADS-B quality index field and extracting an accuracy parameter; calculating trajectory curvature by using a five-point difference method; dynamically calculating a spline smoothing factor in combination with the curvature and the accuracy parameter; generating a position trajectory based on the smoothing factor, and calculating speed, acceleration, and roll angle, pitch angle, and yaw angle attitude parameters to obtain a six-degree-of-freedom trajectory; performing multidimensional dynamic constraint verification on the six-degree-of-freedom trajectory; and adopting a three-stage strategy of preset acceleration establishment, stable maintenance, and deceleration exit on the trajectory meeting the constraint to simulate a roll angle change process in real flight and realize smooth continuity of the roll angle. The application can solve the defects of accuracy-smoothness coupling loss, dynamic constraint loss, and curvature discontinuity in the prior art.

Description

Technical Field

[0001] This invention relates to the field of aircraft monitoring and trajectory processing technology, specifically to a trajectory smoothing system and method based on ADS-B dynamic constraints. Background Technology

[0002] Currently, with the rapid development of the low-altitude economy, the throughput of civil aviation transport airports is increasing year by year, especially large airports, which are becoming increasingly busy. Simultaneously, with the development of the low-altitude economy, the density of low-altitude aircraft operations has increased significantly, posing a potential threat to the operational safety of transport airports. In airport drone prevention systems, the core function is to accurately assess the operational risks of drones and transport aircraft. Testing of this risk assessment function shows that real flight data provides far better support than model-based simulation data. The area within the airport warning zone (a composite area consisting of 9 kilometers outside each end of the runway, 4.5 kilometers on each side of the runway centerline, and an altitude of 500 meters) is a key area for airport drone prevention. Continuous smoothing of civil aviation transport aircraft tracks based on discrete historical data within this area is the core foundation for supporting drone prevention. However, the current ADS-B data transmitted by civil aviation transport aircraft faces the following technical challenges:

[0003] 1. Data noise and accuracy uncertainty: ADS-B reports are affected by accuracy indicators such as NACp (Navigation Accuracy Category for Position) and NACv (Navigation Accuracy Category for Velocity). The positioning and velocity accuracy reported by different aircraft varies significantly (horizontal accuracy ≥18.52km when NACp=0, <3m when NACp=11).

[0004] 2. The aircraft transmits data collected by the sensors via the 1090MHz frequency band. The uncertainty of electromagnetic propagation in the air results in a data interval of about 0.5s and is non-uniform. This does not meet the high-frequency sampling requirements for airport drone prevention risk assessment. It is necessary to increase the data sampling frequency to 30Hz through technology to meet the requirements.

[0005] 3. In ADS-B data, aircraft only transmit longitude, latitude, flight altitude, heading, and roll angle, but not pitch angle information. In most cases, roll angle data is missing. However, airport drone defense requires complete aircraft position and attitude information, and technology is needed to reconstruct the flight attitude information of civil transport aircraft based on flight history data.

[0006] 4. Lack of dynamic constraints: Existing smoothing methods (such as B-splines and cubic splines) only focus on geometric continuity and do not establish a physical mapping relationship between the six degrees of freedom dynamic characteristics of the aircraft (position, velocity, acceleration, roll angle, pitch angle, yaw angle) and the trajectory geometry.

[0007] The existing traditional technical solutions mainly include the following:

[0008] a. Fixed-parameter spline smoothing method: This method uses B-splines or cubic splines to fit the ADS-B trajectory points, and achieves trajectory smoothing by manually adjusting the control point weights. Although this method can guarantee geometric continuity, it lacks correlation with aircraft dynamic parameters, cannot verify whether the generated trajectory meets the physical constraints of the roll angle, and the parameter adjustment relies on manual experience, resulting in low automation.

[0009] b. Dubins / Reeds-Shepp path planning method: This method generates the shortest path consisting of straight segments and circular arc segments of fixed radius based on the minimum turning radius constraint. However, it assumes a constant turning radius and does not consider the aircraft's dynamic turning capabilities at different speeds, leading to generated trajectories that do not match actual flight characteristics.

[0010] c. Inverse calculation method based on flight profile: Vertical profile parameters are determined through inverse calculation using the descent vertex (TOD), providing positional constraints for the horizontal profile. Although this method considers vertical dynamic characteristics, the horizontal profile still uses simple broken line connections, lacking quantitative control over the continuity of track curvature.

[0011] d. Filter smoothing method: Kalman filtering, particle filtering, etc. are used to smooth the ADS-B data in time series. This method can effectively suppress noise, but it does not explicitly model aircraft dynamic constraints, and the filtering parameters need to be manually adjusted according to accuracy indicators such as NACp / NACv, making it difficult to adapt to ADS-B data of different accuracy levels.

[0012] In summary, traditional track smoothing methods have the following obvious drawbacks:

[0013] 1. Missing accuracy-smoothness coupling: Traditional methods do not establish a dynamic mapping relationship between ADS-B accuracy indices (NACp / NACv) and smoothing parameters. Over-smoothing of high-precision data (NACp≥9) leads to loss of details, while insufficient smoothing of low-precision data (NACp≤4) leads to trajectory oscillation.

[0014] 2. Incomplete six-degree-of-freedom dynamic constraint modeling: Existing methods focus primarily on position and velocity constraints, lacking consideration for roll angle. Pitch angle Yaw angle A complete modeling of its rate of change cannot ensure that the generated trajectory conforms to the physical flight characteristics of the aircraft.

[0015] 3. Lack of curvature continuity guarantee mechanism: Traditional methods lack explicit control over trajectory curvature, resulting in abrupt curvature changes in the turning transition zone, which does not conform to the characteristic of continuous curvature changes in actual aircraft flight.

[0016] 4. Simplified roll angle transition process: In actual flight, the roll angle changes follow a three-stage process (acceleration to build up - stability maintenance - deceleration to exit), while traditional methods often assume that the roll angle changes instantaneously, which does not match the actual flight characteristics. Summary of the Invention

[0017] In view of the technical defects mentioned in the background art, the purpose of this invention is to provide a trajectory smoothing system and method based on ADS-B dynamic constraints, so as to solve the defects of lack of accuracy-smoothness coupling, lack of dynamic constraints and curvature discontinuity in traditional trajectory smoothing methods.

[0018] To achieve the above objectives, in a first aspect, embodiments of the present invention provide a trajectory smoothing system based on ADS-B dynamic constraints, the system comprising:

[0019] The coordinate transformation module is used to transform the original ADS-B data into a local rectangular coordinate system to ensure that subsequent geometric calculations are performed in a planar coordinate system.

[0020] The ADS-B precision parsing module is used to parse ADS-B quality indicator fields and extract preset ADS-B precision parameters to construct a precision-uncertainty mapping table.

[0021] The curvature calculation module is used to calculate the trajectory curvature in a local rectangular coordinate system using the five-point difference method; wherein, the trajectory curvature includes the local curvature of the corresponding trajectory;

[0022] The dynamic smoothing parameter calculation module is used to dynamically calculate the spline smoothing factor by combining the local curvature and ADS-B accuracy parameters.

[0023] The six-degree-of-freedom trajectory generation module is used to generate a position trajectory based on the smoothing factor, and calculate the velocity, acceleration, roll angle, pitch angle, and yaw angle attitude parameters to obtain the six-degree-of-freedom trajectory.

[0024] The dynamic constraint verification module is used to perform multi-dimensional dynamic constraint verification on the six-degree-of-freedom trajectory to ensure that the generated trajectory conforms to the physical flight characteristics of the aircraft; if the constraints are not met, the dynamic smoothing parameter calculation module is fed back to readjust the smoothing factor.

[0025] The three-stage roll angle transition module is used to simulate the roll angle change process in real flight by using a preset three-stage strategy of acceleration establishment, stability maintenance and deceleration exit for a trajectory that meets the constraints, so as to achieve smooth and continuous roll angle and output the final smooth six-degree-of-freedom trajectory.

[0026] As a specific implementation of this application, the ADS-B accuracy parameters include NACp, NACv, NIC, NICbaro, and SIL. The accuracy-uncertainty mapping table includes the physical meaning of each accuracy parameter, the 95% confidence error limit, and the application scenario; and includes the mapping relationship between NACp and the horizontal position error limit EPU and the mapping relationship between NACv and the horizontal velocity error limit HV.

[0027] As one specific implementation of this application, the discrete trajectory point sequence The formula for calculating curvature is:

[0028] , The number of trajectory points;

[0029] The first derivative (Speed) uses a five-point central difference:

[0030] h represents the time interval;

[0031] Second derivative (Acceleration) uses a five-point central difference:

[0032] ;

[0033] Boundary points are handled using the three-point or four-point difference method; curvature With turning radius Satisfying Relationship:

[0034] ;

[0035] in This is the curvature threshold to avoid division by zero errors.

[0036] As one specific implementation of this application, the spline smoothing factor The calculation formula is:

[0037] ;

[0038] Where K is the local curvature, calculated using the curvature calculation formula; the smoothing factor is adjusted using an exponential curvature decay method.

[0039] The minimum smoothing factor for the turning segment;

[0040] The maximum smoothing factor for the line segment;

[0041] This is the curvature sensitivity coefficient;

[0042] The maximum curvature of the trajectory;

[0043] The accuracy adaptive coefficient is the coefficient of performance. Defined as:

[0044] ;

[0045] To achieve the optimal balance between accuracy and smoothness.

[0046] As a specific implementation of this application, the six-degree-of-freedom trajectory generation module includes a position trajectory generation unit and a parameter calculation unit;

[0047] The position trajectory generation unit is used to employ a piecewise smoothing strategy to first generate a preliminary smoothed trajectory using UnivariateSpline for the downsampled trajectory points, and then perform final smoothing using CubicSpline to ensure the continuity of the second derivative.

[0048] The parameter calculation unit is used for:

[0049] Velocity and acceleration were calculated using the five-point difference method.

[0050] Based on Newton's second law and the centripetal force formula, a physical mapping between the roll angle and curvature and velocity is established to calculate the roll angle.

[0051] Calculate the pitch angle based on the ratio of vertical velocity to horizontal velocity;

[0052] The yaw angle is calculated based on the velocity vector direction.

[0053] As a specific implementation of this application, the multi-dimensional dynamic constraints of the dynamic constraint verification module include velocity constraints, acceleration constraints, roll angle constraints, and curvature continuity constraints;

[0054] The curvature continuity constraint includes inter-segment distance constraints and angular continuity constraints.

[0055] ;in, Indicates the distance constraint between segments; Indicates the end point of the turn; Indicates the starting point of the turn; Represents the discrete segmentation distance;

[0056] ;in, Indicates angular continuity constraints; , Indicates two tangents along the trajectory; Indicates the turning angle threshold;

[0057] Angle difference Calculate quickly using the following methods:

[0058] .

[0059] As a specific implementation of this application, in the three-stage roll angle transition module, the three-stage function of the roll angle along the arc length s is:

[0060]

[0061] in, To obtain the maximum roll angle through optimization;

[0062] (5° / s) represents the typical roll rate of a civil aircraft.

[0063] , indicating the arc length of the acceleration / deceleration phase;

[0064] To maintain the stage arc length, it is determined by the total arc length of the turn;

[0065] The speed is horizontal.

[0066] Secondly, embodiments of the present invention also provide a trajectory smoothing method based on ADS-B dynamic constraints, applied to a trajectory smoothing system based on ADS-B dynamic constraints as described in the first aspect, the method comprising the following steps:

[0067] The original ADS-B data is transformed to obtain a local rectangular coordinate system, so as to ensure that subsequent geometric calculations are performed in a planar coordinate system.

[0068] Parse the ADS-B quality index fields and extract the preset ADS-B accuracy parameters to construct an accuracy-uncertainty mapping table;

[0069] The trajectory curvature in a local rectangular coordinate system is calculated using the five-point difference method; wherein, the trajectory curvature includes the local curvature of the corresponding trajectory;

[0070] The spline smoothing factor is dynamically calculated by combining the local curvature and ADS-B accuracy parameters.

[0071] The position trajectory is generated based on the smoothing factor, and the velocity, acceleration, roll angle, pitch angle and yaw angle attitude parameters are calculated to obtain a six-degree-of-freedom trajectory.

[0072] The six-degree-of-freedom trajectory is subjected to multi-dimensional dynamic constraint verification to ensure that the generated trajectory conforms to the physical flight characteristics of the aircraft; if the constraints are not met, the smoothing factor is readjusted.

[0073] For the trajectory that meets the constraints, a preset three-stage strategy of acceleration establishment, stability maintenance and deceleration exit is adopted to simulate the roll angle change process in real flight, realize the smooth and continuous roll angle, and output the final smooth six-degree-of-freedom trajectory.

[0074] The technical solution provided by this invention constructs a joint smoothing parameter calculation formula for curvature and accuracy, and automatically adjusts the smoothing intensity according to the ADS-B accuracy index to achieve an optimal balance between accuracy and smoothness. Furthermore, the generated trajectory strictly adheres to the six-degree-of-freedom dynamic constraints of the aircraft, particularly the physical limitations of the roll angle, and employs a three-stage roll angle transition strategy to simulate real flight characteristics, ensuring that the trajectory is not only geometrically continuous but also conforms to actual flight capabilities, thus improving the credibility of simulation evaluation. Simultaneously, a dual verification mechanism for inter-segment distance and angle continuity is designed to strictly control the smoothness of the trajectory, ensuring curvature continuity and significantly reducing the risk of abrupt changes in heading. The heading changes at waypoint connections are smooth and continuous, resulting in a significant improvement in the geometric continuity of the trajectory. Attached Figure Description

[0075] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below.

[0076] Figure 1 This is a principle block diagram of a trajectory smoothing system based on ADS-B dynamic constraints provided in an embodiment of the present invention;

[0077] Figure 2 This is a schematic diagram of a trajectory smoothing system based on ADS-B dynamic constraints provided in an embodiment of the present invention;

[0078] Figure 3 This is a schematic diagram of a three-stage roll angle transition strategy provided in an embodiment of the present invention;

[0079] Figure 4 This is a three-dimensional image of raw data provided in an embodiment of the present invention;

[0080] Figure 5 This is a smooth trajectory three-dimensional graph provided in an embodiment of the present invention;

[0081] Figure 6This is a time-to-ground velocity diagram provided by an embodiment of the present invention;

[0082] Figure 7 This is a time-altitude variation diagram provided in an embodiment of the present invention;

[0083] Figure 8 This is a time-heading comparison chart provided in an embodiment of the present invention;

[0084] Figure 9 This is a time-pitch and roll angle variation graph provided in an embodiment of the present invention;

[0085] Figure 10 This is a flowchart of a trajectory smoothing method with ADS-B dynamic constraints provided in an embodiment of the present invention. Detailed Implementation

[0086] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0087] It should be understood that, when used in this specification and the appended claims, the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0088] Throughout this specification, references to "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, the phrases "in an embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination.

[0089] ADS-B: Automatic Dependent Surveillance-Broadcast.

[0090] It should be noted that, unless otherwise stated, the technical terms used in this embodiment have the common meaning as understood in the relevant technical field.

[0091] Please refer to Figures 1 to 3This invention provides a trajectory smoothing system based on ADS-B dynamic constraints, the system comprising:

[0092] The coordinate transformation module is used to transform the original ADS-B data into a local rectangular coordinate system to ensure that subsequent geometric calculations are performed in a planar coordinate system.

[0093] The ADS-B precision parsing module is used to parse ADS-B quality indicator fields and extract preset ADS-B precision parameters to construct a precision-uncertainty mapping table.

[0094] The curvature calculation module is used to calculate the trajectory curvature in a local rectangular coordinate system using the five-point difference method; wherein, the trajectory curvature includes the local curvature of the corresponding trajectory;

[0095] The dynamic smoothing parameter calculation module is used to dynamically calculate the spline smoothing factor by combining the local curvature and ADS-B accuracy parameters.

[0096] The six-degree-of-freedom trajectory generation module is used to generate a position trajectory based on the smoothing factor, and calculate the velocity, acceleration, roll angle, pitch angle, and yaw angle attitude parameters to obtain the six-degree-of-freedom trajectory.

[0097] The dynamic constraint verification module is used to perform multi-dimensional dynamic constraint verification on the six-degree-of-freedom trajectory to ensure that the generated trajectory conforms to the physical flight characteristics of the aircraft; if the constraints are not met, the dynamic smoothing parameter calculation module is fed back to readjust the smoothing factor.

[0098] The three-stage roll angle transition module is used to simulate the roll angle change process in real flight by using a preset three-stage strategy of acceleration establishment, stability maintenance and deceleration exit for a trajectory that meets the constraints, so as to achieve smooth and continuous roll angle and output the final smooth six-degree-of-freedom trajectory.

[0099] In this embodiment, when the coordinate transformation module is applied, it uses the Transverse Mercator projection to convert the WGS84 latitude and longitude coordinate system into a local rectangular coordinate system while maintaining angular invariance.

[0100]

[0101] in:

[0102] The radius of the Earth's equator;

[0103] The latitude and longitude of the projection origin (usually the starting waypoint);

[0104] The coordinates of the point to be converted are latitude and longitude.

[0105] Local rectangular coordinates ( The axis points due east. (The axis points due north).

[0106] This transformation ensures that subsequent geometric calculations are performed in a planar coordinate system, improving computational efficiency and accuracy; for the height dimension, the geometric height (I021 / 140) or barometric altitude (I021 / 145) reported by ADS-B is used directly.

[0107] In the ADS-B accuracy analysis module, this module parses the ADS-B quality index field (I021 / 090), extracts accuracy parameters such as NACp, NACv, NIC, NICbaro, and SIL, and constructs an accuracy-uncertainty mapping table, as detailed in Table 1.

[0108] Mapping relationship between NACp and horizontal position error limit EPU:

[0109] ;

[0110] NACv and horizontal velocity error limits Mapping relationship:

[0111] .

[0112] Table 1 Accuracy-Uncertainty Mapping Table

[0113] Accuracy indicators Physical meaning 95% confidence level margin of error Application scenarios NACp Location navigation accuracy category level: vertical: Trajectory position smoothing intensity control NACv Speed ​​navigation accuracy category Horizontal speed: Vertical velocity: Velocity derivative calculation weight adjustment NIC Navigation integrity category Horizontal radius tolerance: Safety Interval Calculation NICbaro Baroque Integrity 0: No cross-validation 1: Cross-validation High-level data reliability assessment SIL Monitoring Integrity Level Probability of undetected error: High integrity scene filtering

[0114] In this embodiment, the five-point difference method is used to calculate the trajectory curvature, avoiding the instability problem of the traditional three-point difference method under noisy data; the application of existing technologies in the five-point difference method will not be elaborated here.

[0115] The discrete trajectory point sequence The formula for calculating curvature is:

[0116] , The number of trajectory points;

[0117] The first derivative (Speed) uses a five-point central difference:

[0118] h represents the time interval;

[0119] Second derivative (Acceleration) uses a five-point central difference:

[0120] ;

[0121] Boundary points are handled using the three-point or four-point difference method; curvature With turning radius Satisfying Relationship:

[0122] ;

[0123] in This is the curvature threshold to avoid division by zero errors.

[0124] spline smoothing factor The calculation formula is:

[0125] ;

[0126] Wherein, K is the local curvature, which is calculated using the curvature calculation formula; the smoothing factor is adjusted by the curvature exponential decay method; since the aircraft will make several turns during flight, each turn is a local area, and each local area has a corresponding local curvature, which is still calculated using the aforementioned curvature calculation formula.

[0127] The minimum smoothing factor for the turning segment;

[0128] The maximum smoothing factor for the line segment;

[0129] This is the curvature sensitivity coefficient;

[0130] The maximum curvature of the trajectory;

[0131] The accuracy adaptive coefficient is the coefficient of performance. Defined as:

[0132] ;

[0133] To achieve the optimal balance between accuracy and smoothness;

[0134] An adaptive mapping mechanism between ADS-B accuracy metrics and smoothing parameters is implemented, which ensures that:

[0135] High curvature areas (sharp turns) use small Values ​​that preserve the turning geometry;

[0136] Low curvature regions (straight segments) use large Value, suppressing noise;

[0137] For low-precision data (NACp≤4), the overall smoothing intensity is enhanced;

[0138] High-precision data (NACp≥9) retains more trajectory details.

[0139] In application, the six-degree-of-freedom trajectory generation module includes a position trajectory generation unit and a parameter calculation unit.

[0140] The position trajectory generation unit is used to employ a piecewise smoothing strategy to first generate a preliminary smoothed trajectory using UnivariateSpline for the downsampled trajectory points, and then perform final smoothing using CubicSpline to ensure the continuity of the second derivative.

[0141] Specifically, a piecewise smoothing strategy is adopted for the downsampled trajectory points (time intervals). Apply UnivariateSpline to generate an initial smooth trajectory: ;

[0142] in, Based on XY plane curvature calculation For fixed height smoothing parameters;

[0143] The initial smoothed trajectory is then smoothed using CubicSpline for final smoothing, ensuring the continuity of the second derivative: ;

[0144] The parameter calculation unit is used for:

[0145] Velocity and acceleration were calculated using the five-point difference method.

[0146] Based on Newton's second law and the centripetal force formula, a physical mapping between the roll angle and curvature and velocity is established to calculate the roll angle.

[0147] Calculate the pitch angle based on the ratio of vertical velocity to horizontal velocity;

[0148] The yaw angle is calculated based on the velocity vector direction.

[0149] In application, velocity and acceleration calculations

[0150] Speed ​​calculation using the five-point difference method and acceleration :

[0151] , ;

[0152] Horizontal speed magnitude:

[0153] ;

[0154] Roll angle calculation

[0155] Based on Newton's second law and the centripetal force formula, the roll angle is established. With curvature ,speed Physical mapping:

[0156] ;

[0157] in This is the acceleration due to gravity. This formula ensures that the generated trajectory conforms to the aircraft's turning dynamics constraints.

[0158] Pitch angle calculation

[0159] Pitch angle is calculated based on the ratio of vertical velocity to horizontal velocity. :

[0160] ;

[0161] Yaw angle calculation

[0162] Calculate yaw angle based on velocity vector direction (Heading angle):

[0163] .

[0164] Furthermore, the multi-dimensional dynamic constraints of the dynamic constraint verification module include velocity constraints, acceleration constraints, roll angle constraints, and curvature continuity constraints;

[0165] Speed ​​constraints

[0166] ;

[0167] Acceleration constraints

[0168] ;

[0169] Roll angle constraint

[0170] ;

[0171] The curvature continuity constraint includes inter-segment distance constraints and angular continuity constraints.

[0172] ;in, Indicates the distance constraint between segments; Indicates the end point of the turn; Indicates the starting point of the turn; Represents the discrete segmentation distance;

[0173] Angular continuity constraint (based on three connection points):

[0174] ;in, Indicates angular continuity constraints; , Indicates two tangents along the trajectory; Indicates the turning angle threshold;

[0175] Angle difference Calculate quickly using the following methods:

[0176] .

[0177] If the trajectory does not meet the above constraints, the smoothing parameter adaptive adjustment mechanism is triggered to regenerate the trajectory until all constraints are met.

[0178] In this embodiment, to avoid abrupt changes in roll angle, a three-stage roll angle transition strategy is proposed to simulate the roll angle change process in real flight.

[0179] Among them, roll angle A three-stage function along arc length s:

[0180]

[0181] in, To obtain the maximum roll angle through optimization;

[0182] (5° / s) represents the typical roll rate of a civil aircraft.

[0183] , indicating the arc length of the acceleration / deceleration phase;

[0184] To maintain the stage arc length, it is determined by the total arc length of the turn;

[0185] The speed is horizontal.

[0186] The above scheme achieves an optimal balance between accuracy and smoothness by constructing a joint smoothing parameter calculation formula for curvature and accuracy, and automatically adjusting the smoothing intensity based on the ADS-B accuracy index. Furthermore, the generated trajectory strictly adheres to the six-degree-of-freedom dynamic constraints of the aircraft, particularly the physical limitations of the roll angle, and employs a three-stage roll angle transition strategy to simulate real flight characteristics. This ensures that the trajectory is not only geometrically continuous but also conforms to actual flight capabilities, improving the reliability of simulation evaluation. Simultaneously, a dual verification mechanism for inter-segment distance and angular continuity is designed to strictly control the smoothness of the trajectory, ensuring curvature continuity and significantly reducing the risk of abrupt changes in heading. The heading changes at waypoint connections are smooth and continuous, resulting in a significant improvement in the geometric continuity of the trajectory.

[0187] To facilitate understanding of this solution, the following example is provided.

[0188] Example 1: ADS-B data smoothing during takeoff

[0189] Input data:

[0190] Flight address: 7816xx;

[0191] Flight number: CSN66xx;

[0192] Number of track points: 18,317 (time span from 1703,355,152.942 to 1703,397,231.422, totaling 42,078.48 seconds);

[0193] The average values ​​are NUCr / NACv = 1, NUCp / NIC = 8, NICbaro = 1, SIL = 3, and NACp = 9.

[0194] Flight phase: from taxiing to takeoff and cruise.

[0195] Processing results reference Figures 4 to 9 ;in, Figure 6 and Figure 7 In the diagram, red represents the original data, dashed lines represent the measurement error range, and blue represents the smoothing trajectory. Figure 8 In the diagram, red indicates the TA (Transmission Heading), yellow indicates the filtered heading, and green indicates the calculated heading. Figure 9 In the diagram, purple represents the roll angle and green represents the pitch angle.

[0196] Result verification:

[0197] A total of 19,560 points were generated;

[0198] Planning time: 1.70 seconds (meets real-time requirements);

[0199] Horizontal position error: RMSE = 3.571 m (better than 30 m accuracy with NACp = 9);

[0200] Vertical position error: RMSE = 0.305 m (better than 7.62 m resolution accuracy);

[0201] Speed ​​error: RMSE = 1.01 m / s (better than the 10 m / s accuracy of NACv = 1).

[0202] Maximum roll angle: 7.141°.

[0203] Example 2: ADS-B data smoothing during the landing phase

[0204] Input data:

[0205] Flight address: 8xxCAF;

[0206] Flight number: SJO2xx;

[0207] Number of track points: 3988 (time span 2388.9 seconds);

[0208] The average values ​​are NUCr / NACv = 0, NUCp / NIC = 6, NICbaro = 0, SIL = 2, and NACp = 0.

[0209] Flight phases: the entire process from cruise to landing.

[0210] The process of processing the results is similar to that in Example 1.

[0211] Result verification:

[0212] ① A total of 23,890 points were generated;

[0213] ② Planning time: 0.75 seconds (meets real-time requirements);

[0214] ③ Horizontal position error: RMSE=8.03 m (better than the accuracy of more than 1852 m with NACp=0);

[0215] ④ Vertical position error: RMSE = 0.450 m (better than 7.62 m resolution accuracy);

[0216] ⑤ Speed ​​error: RMSE=0.95 m / s (better than the accuracy of greater than 10 m / s with NACv=1).

[0217] Maximum roll angle: 0.307°.

[0218] Based on the same inventive concept, this embodiment of the invention also provides a trajectory smoothing method based on ADS-B dynamic constraints, applied to the trajectory smoothing system based on ADS-B dynamic constraints described in the first aspect, with reference to... Figure 10 The method includes the following steps:

[0219] S101 transforms the original ADS-B data to obtain a transformed local rectangular coordinate system, ensuring that subsequent geometric calculations are performed in a planar coordinate system;

[0220] S102, parse the ADS-B quality index fields and extract the preset ADS-B accuracy parameters to construct an accuracy-uncertainty mapping table;

[0221] S103, The five-point difference method is used to calculate the trajectory curvature in the local rectangular coordinate system; wherein, the trajectory curvature includes the local curvature of the corresponding trajectory;

[0222] S104, Combining the local curvature and ADS-B accuracy parameters, dynamically calculate the spline smoothing factor;

[0223] S105, Based on the smoothing factor, generate the position trajectory and calculate the velocity, acceleration, roll angle, pitch angle and yaw angle attitude parameters to obtain the six-degree-of-freedom trajectory;

[0224] S106, Perform multi-dimensional dynamic constraint verification on the six-degree-of-freedom trajectory to ensure that the generated trajectory conforms to the physical flight characteristics of the aircraft; if the constraints are not met, readjust the smoothing factor.

[0225] S107 employs a preset three-stage strategy of acceleration establishment, stability maintenance, and deceleration exit for the trajectory that meets the constraints, simulating the roll angle change process in real flight, achieving smooth and continuous roll angle, and outputting the final smooth six-degree-of-freedom trajectory.

[0226] Furthermore, the spline smoothing factor The calculation formula is:

[0227] ;

[0228] Where K is the local curvature, calculated using the curvature calculation formula; the smoothing factor is adjusted using an exponential curvature decay method.

[0229] The minimum smoothing factor for the turning segment;

[0230] The maximum smoothing factor for the line segment;

[0231] This is the curvature sensitivity coefficient;

[0232] The maximum curvature of the trajectory;

[0233] The accuracy adaptive coefficient is the coefficient of performance. Defined as:

[0234] ;

[0235] To achieve the optimal balance between accuracy and smoothness.

[0236] In this embodiment, the multi-dimensional dynamic constraints include velocity constraints, acceleration constraints, roll angle constraints, and curvature continuity constraints;

[0237] The curvature continuity constraint includes inter-segment distance constraints and angular continuity constraints.

[0238] ;in, Indicates the distance constraint between segments; Indicates the end point of the turn; Indicates the starting point of the turn; Represents the discrete segmentation distance;

[0239] ;in, Indicates angular continuity constraints; , Indicates two tangents along the trajectory; Indicates the turning angle threshold;

[0240] Angle difference Calculate quickly using the following methods:

[0241] .

[0242] The three-stage strategy simulates the roll angle change process in real flight by constructing a three-stage function of the roll angle along the arc length s. The three-stage function is as follows:

[0243]

[0244] in, To obtain the maximum roll angle through optimization;

[0245] (5° / s) represents the typical roll rate of a civil aircraft.

[0246] , indicating the arc length of the acceleration / deceleration phase;

[0247] To maintain the stage arc length, it is determined by the total arc length of the turn;

[0248] The speed is horizontal.

[0249] It should be noted that for a more detailed description of the workflow of the method embodiments, please refer to the aforementioned system embodiments section, which will not be repeated here.

[0250] The specific benefits of the entire scheme include: 1. Significantly improved trajectory geometric continuity.

[0251] The generated trajectory exhibits smooth and continuous heading changes at waypoint junctions, with the maximum angle difference being minimal. This significantly reduces the risk of sudden course changes and improves flight safety and comfort.

[0252] Corresponding technical solution:

[0253] The curvature adaptive smoothing parameter is dynamically adjusted to ensure continuous curvature change in the turning transition zone;

[0254] The design incorporates a dual verification mechanism for inter-segment distance and angle continuity to strictly control the smoothness of the flight path;

[0255] A three-stage roll angle transition strategy is used to eliminate roll angle mutations.

[0256] 2. The physical realism of the trajectory has been greatly improved.

[0257] The generated trajectory strictly follows the six-degree-of-freedom dynamic constraints of the aircraft, especially the physical limitations of the roll angle, ensuring that the trajectory is not only geometrically continuous but also conforms to actual flight capabilities, thereby improving the credibility of simulation evaluation.

[0258] Corresponding technical solution:

[0259] Establish roll angle With curvature ,speed Dynamic mapping model ;

[0260] Roll angle constraint Embedded trajectory generation process;

[0261] A three-stage roll angle transition strategy is adopted to simulate real flight characteristics.

[0262] 3. Accuracy-Smoothness Adaptive Balance

[0263] The smoothing intensity is automatically adjusted based on the ADS-B accuracy index (NACp / NACv), preserving details for high-precision data and enhancing smoothness for low-precision data, achieving the optimal balance between accuracy and smoothness.

[0264] Corresponding technical solution:

[0265] Design accuracy adaptive coefficient When NACp≤4 (Enhanced smoothing), when NACp≥9 (Details retained);

[0266] Constructing a curvature-accuracy joint smoothing parameter calculation model ;

[0267] Weights are calculated based on the dynamic adjustment of the velocity derivative using NACv.

[0268] 4. High computational efficiency, meeting the requirements of real-time simulation.

[0269] Complex trajectory smoothing is completed within milliseconds, meeting the real-time trajectory prediction requirements for low-altitude operation scenarios.

[0270] Corresponding technical solution:

[0271] Geometric algorithms (spline interpolation) are used to replace complex numerical optimization.

[0272] By downsampling ( Reduce the number of calculation points;

[0273] Vectorized computation optimization key steps (curvature calculation, derivative calculation).

[0274] 5. High degree of automation, requiring no human intervention.

[0275] It automatically adapts to ADS-B data of different accuracy levels and trajectory characteristics of different flight stages without the need for manual adjustment of smoothing parameters.

[0276] Corresponding technical solution:

[0277] Design a complete closed-loop process for trajectory generation, verification, and optimization;

[0278] Automatically adjust smoothing parameters based on the degree of constraint violation;

[0279] The pre-validation mechanism ensures that the algorithm converges within a reasonable time.

[0280] By integrating ADS-B accuracy indicators, curvature adaptive mechanisms, and six-degree-of-freedom dynamic constraints, this method solves the technical problems existing in traditional trajectory smoothing methods, such as accuracy-smoothness imbalance, lack of dynamic constraints, and curvature discontinuity. This method has the advantages of high trajectory geometric continuity, good physical realism, high computational efficiency, and high degree of automation. It is particularly suitable for scenarios such as low-altitude aircraft operation monitoring, UAV prevention systems, and arrival and departure flight procedure simulation, and has important application value for improving the safety level of low-altitude operations.

[0281] In the embodiments provided in this application, it should be understood that the disclosed systems and methods can also be implemented in other ways. The embodiments described above are merely illustrative. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the figures. For example, two consecutive blocks may actually be executed substantially in parallel, or they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, and combinations of blocks in the block diagram and / or flowchart, can be implemented using a dedicated hardware-based system that performs the specified functions or actions, or using a combination of dedicated hardware and computer instructions.

[0282] Furthermore, the functional modules in the various embodiments of this invention can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part. When using each module, information is collected and stored only with the full authorization of the relevant user or organization and in compliance with relevant laws and regulations, and the security and privacy of the data are protected. Unauthorized access is strictly prohibited. Data processing will be carried out within the scope stipulated by law and will not exceed the authorized purpose and scope. At the same time, the authorizing party has the right to access, correct, delete, restrict processing, refuse, etc., of its personal data, and strictly comply with applicable laws and regulations and conduct compliance reviews.

[0283] If the aforementioned functions are implemented as software functional modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. For those skilled in the art, this invention can have various modifications and variations. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A trajectory smoothing system based on ADS-B dynamic constraints, characterized in that, The system includes: The coordinate transformation module is used to transform the original ADS-B data into a local rectangular coordinate system to ensure that subsequent geometric calculations are performed in a planar coordinate system. The ADS-B precision parsing module is used to parse ADS-B quality indicator fields and extract preset ADS-B precision parameters to construct a precision-uncertainty mapping table. The curvature calculation module is used to calculate the trajectory curvature in a local rectangular coordinate system using the five-point difference method; wherein, the trajectory curvature includes the local curvature of the corresponding trajectory; The dynamic smoothing parameter calculation module is used to dynamically calculate the spline smoothing factor by combining the local curvature and ADS-B accuracy parameters. The six-degree-of-freedom trajectory generation module is used to generate a position trajectory based on the smoothing factor, and calculate the velocity, acceleration, roll angle, pitch angle, and yaw angle attitude parameters to obtain the six-degree-of-freedom trajectory. The dynamic constraint verification module is used to perform multi-dimensional dynamic constraint verification on the six-degree-of-freedom trajectory to ensure that the generated trajectory conforms to the physical flight characteristics of the aircraft; if the constraints are not met, the dynamic smoothing parameter calculation module is fed back to readjust the smoothing factor. The three-stage roll angle transition module is used to simulate the roll angle change process in real flight by using a preset three-stage strategy of acceleration establishment, stability maintenance and deceleration exit for a trajectory that meets the constraints, so as to achieve smooth and continuous roll angle and output the final smooth six-degree-of-freedom trajectory.

2. The system as described in claim 1, characterized in that, The ADS-B accuracy parameters include NACp, NACv, NIC, NICbaro, and SIL. The accuracy-uncertainty mapping table includes the physical meaning of each accuracy parameter, the 95% confidence error limit, and application scenarios; and includes the mapping relationship between NACp and the horizontal position error limit EPU and the mapping relationship between NACv and the horizontal velocity error limit HV.

3. The system as described in claim 1, characterized in that, The discrete trajectory point sequence The formula for calculating curvature is: , The number of trajectory points; The first derivative (Speed) uses a five-point central difference: h represents the time interval; Second derivative (Acceleration) uses a five-point central difference: ； Boundary points are handled using the three-point or four-point difference method; curvature With turning radius Satisfying Relationship: ； in This is the curvature threshold to avoid division by zero errors.

4. The system as described in claim 3, characterized in that, spline smoothing factor The calculation formula is: ； Where K is the local curvature, calculated using the curvature calculation formula; the smoothing factor is adjusted using an exponential curvature decay method. The minimum smoothing factor for the turning segment; The maximum smoothing factor for the line segment; This is the curvature sensitivity coefficient; The maximum curvature of the trajectory; The accuracy adaptive coefficient is the coefficient of performance. Defined as: ； To achieve the optimal balance between accuracy and smoothness.

5. The system as described in any one of claims 1 to 4, characterized in that, The six-degree-of-freedom trajectory generation module includes a position trajectory generation unit and a parameter calculation unit; The position trajectory generation unit is used to employ a piecewise smoothing strategy to first generate a preliminary smoothed trajectory using UnivariateSpline for the downsampled trajectory points, and then perform final smoothing using CubicSpline to ensure the continuity of the second derivative. The parameter calculation unit is used for: Velocity and acceleration were calculated using the five-point difference method. Based on Newton's second law and the centripetal force formula, a physical mapping between the roll angle and curvature and velocity is established to calculate the roll angle. Calculate the pitch angle based on the ratio of vertical velocity to horizontal velocity; The yaw angle is calculated based on the velocity vector direction.

6. The system as described in claim 5, characterized in that, The multi-dimensional dynamic constraints of the dynamic constraint verification module include velocity constraints, acceleration constraints, roll angle constraints, and curvature continuity constraints. The curvature continuity constraint includes inter-segment distance constraints and angular continuity constraints. ;in, Indicates the distance constraint between segments; Indicates the end point of the turn; Indicates the starting point of the turn; Represents the discrete segmentation distance; ;in, Indicates angular continuity constraints; , Indicates two tangents along the trajectory; Indicates the turning angle threshold; Angle difference Calculate quickly using the following methods: 。 7. The system as described in claim 6, characterized in that, In the three-stage roll angle transition module, the three-stage function of the roll angle along the arc length s is: in, To obtain the maximum roll angle through optimization; (5° / s) represents the typical roll rate of a civil aircraft. , indicating the arc length of the acceleration / deceleration phase; To maintain the stage arc length, it is determined by the total arc length of the turn; The speed is horizontal.

8. A trajectory smoothing method based on ADS-B dynamic constraints, characterized in that, The method applied to the trajectory smoothing system based on ADS-B dynamic constraints as described in claim 1 includes the following steps: The original ADS-B data is transformed to obtain a local rectangular coordinate system, so as to ensure that subsequent geometric calculations are performed in a planar coordinate system. Parse the ADS-B quality index fields and extract the preset ADS-B accuracy parameters to construct an accuracy-uncertainty mapping table; The trajectory curvature in a local rectangular coordinate system is calculated using the five-point difference method; wherein, the trajectory curvature includes the local curvature of the corresponding trajectory; The spline smoothing factor is dynamically calculated by combining the local curvature and ADS-B accuracy parameters. The position trajectory is generated based on the smoothing factor, and the velocity, acceleration, roll angle, pitch angle and yaw angle attitude parameters are calculated to obtain a six-degree-of-freedom trajectory. The six-degree-of-freedom trajectory is subjected to multi-dimensional dynamic constraint verification to ensure that the generated trajectory conforms to the physical flight characteristics of the aircraft; if the constraints are not met, the smoothing factor is readjusted. For the trajectory that meets the constraints, a preset three-stage strategy of acceleration establishment, stability maintenance and deceleration exit is adopted to simulate the roll angle change process in real flight, realize the smooth and continuous roll angle, and output the final smooth six-degree-of-freedom trajectory.

9. The method as described in claim 8, characterized in that, spline smoothing factor The calculation formula is: ； Where K is the local curvature, calculated using the curvature calculation formula; the smoothing factor is adjusted using an exponential curvature decay method. The minimum smoothing factor for the turning segment; The maximum smoothing factor for the line segment; This is the curvature sensitivity coefficient; The maximum curvature of the trajectory; The accuracy adaptive coefficient is the coefficient of performance. Defined as: ； To achieve the optimal balance between accuracy and smoothness.

10. The method as described in claim 8 or 9, characterized in that, The three-stage strategy simulates the roll angle change process in real flight by constructing a three-stage function of the roll angle along the arc length s. The three-stage function is as follows: in, To obtain the maximum roll angle through optimization; (5° / s) represents the typical roll rate of a civil aircraft. , indicating the arc length of the acceleration / deceleration phase; To maintain the stage arc length, it is determined by the total arc length of the turn; The speed is horizontal.

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