A trajectory smoothing method, device, embedded system and storage medium

Abstract

The application provides a trajectory smoothing method, device, embedded system and storage medium, the method comprising: collecting spatial position coordinates of an aircraft at each moment during flight to obtain trajectory data, the trajectory data being represented as a three-dimensional discrete trajectory sequence; performing discrete wavelet decomposition on the discrete trajectory sequence in each dimension to obtain low-frequency components and high-frequency components; performing denoising processing on each layer of high-frequency components using an adaptive threshold to obtain denoised high-frequency components; and performing inverse wavelet transformation on the corrected low-frequency components and the denoised high-frequency components to obtain smoothed trajectory data. In the technical solution provided by the application, high-frequency noise and real motion components in the aircraft trajectory data are effectively separated based on wavelet multiscale decomposition, precise denoising is achieved, and key trajectory details such as rapid maneuvering and mutation of the aircraft are retained as much as possible, thereby effectively avoiding the loss of details and trajectory blurring caused by 'overfitting' in traditional global fitting methods.

Description

Technical Field

[0001] This invention relates to the field of trajectory processing technology, and more specifically to a trajectory smoothing method, apparatus, embedded system, and storage medium. Background Technology

[0002] In related technologies, commonly used trajectory smoothing and denoising methods include B-spline fitting, polynomial curves, Kalman filtering, Wiener filtering, dynamic threshold elimination and interpolation, and differential geometry trajectory optimization. Although the above algorithms improve the smoothness and engineering usability of aircraft trajectory data to a certain extent, the following prominent technical bottlenecks and limitations still exist in practical applications. First, the ability to suppress high-frequency noise and micro-amplitude disturbances is limited. Existing global fitting methods (such as B-splines and polynomials) cannot achieve the separation and processing of different frequency components. High-frequency noise and local micro-amplitude disturbances in the acquired signals are often directly included in the fitted trajectory, resulting in non-physical oscillations and pseudo-maneuvers in the smoothing results. Their adaptive suppression and separation capabilities for complex background noise and multi-source measurement disturbances are severely insufficient. Second, the ability to distinguish between outliers and real maneuvers is weak. Methods such as dynamic threshold criteria, sliding window methods, and interpolation reconstruction rely on static thresholds or simple statistical rules to eliminate outliers, making it difficult to accurately distinguish between sampling errors, sensor anomalies, and real high-speed maneuvering behavior. Overly simplistic anomaly detection can easily lead to false positives or false negatives, threatening the authenticity and integrity of the trajectory during high-maneuverability flight. Thirdly, multi-scale feature compatibility is poor. Traditional smoothing and filtering methods can only operate at a single spatiotemporal scale, lacking effective coordination of multi-scale features such as slow-changing trends (low frequency) and sudden disturbances (high frequency) and local details that exist simultaneously in the trajectory. This results in either loss of details or distortion of the global trend, making it difficult to balance local sensitivity and global smoothness. Summary of the Invention

[0003] In view of the above problems, embodiments of the present invention provide a trajectory smoothing method, apparatus, embedded system, and storage medium to solve the problem that it is difficult to balance local sensitivity and global smoothness in the prior art.

[0004] In a first aspect, embodiments of the present invention provide a trajectory smoothing method, the method comprising: The spatial position coordinates of the aircraft at various moments during flight are collected to obtain trajectory data, which is represented as a three-dimensional discrete trajectory sequence. Discrete wavelet decomposition is performed on the discrete trajectory sequence in each dimension to obtain low-frequency and high-frequency components; An adaptive threshold is used to denoise each high-frequency component to obtain the denoised high-frequency components. The corrected low-frequency component and the denoised high-frequency component are subjected to inverse wavelet transform to obtain smooth trajectory data.

[0005] In one possible implementation, the step of employing an adaptive threshold to denoise each layer of high-frequency components to obtain denoised high-frequency components includes: The noise standard deviation is estimated based on the median absolute deviation of the high-frequency components; Based on the noise standard deviation, the sampling frequency of the trajectory data, and the number of sampling points, a base threshold value is set; the adaptive threshold is the product of the threshold coefficient and the base threshold value. If the noise ratio is less than the first preset ratio, then the threshold coefficient is lowered, and the adaptive threshold is lowered. If the noise ratio is greater than the second preset ratio, then the threshold coefficient is increased to adjust the adaptive threshold. The noise ratio is used to indicate the proportion of sampling points whose amplitude is less than the threshold base value out of the total number of sampling points.

[0006] In one possible implementation, the high-frequency components simultaneously contain Gaussian noise and impulse noise. The step of employing an adaptive threshold to denoise each layer of high-frequency components to obtain denoised high-frequency components includes: The dominant noise type is determined by the kurtosis and peak factor of the high-frequency components; For shallow high-frequency components, if the dominant noise type is impulse noise, hard thresholding is used for denoising; if the dominant noise type is Gaussian noise, soft thresholding is used for denoising. For deep high-frequency components, an improved Garrote threshold is used for denoising to obtain the denoised high-frequency components.

[0007] In one possible implementation, before performing inverse wavelet transform on the corrected low-frequency component and the denoised high-frequency component to obtain smooth trajectory data, the method further includes: A low-order polynomial is used to locally fit the low-frequency components to obtain a trend fitting curve; The 3σ criterion is used to determine whether the residual between the low-frequency component and the trend fitting curve is a low-frequency disturbance. If the residual is determined to be a low-frequency disturbance, the low-frequency component is corrected using the trend fitting curve. The time-frequency synchronization of the corrected low-frequency component and the denoised high-frequency component is checked.

[0008] In one possible implementation, before performing discrete wavelet decomposition on the discrete trajectory sequence in each dimension, the following is also included: The initial core parameters are determined based on the sampling frequency and average velocity. The initial core parameters are dynamically adjusted based on the actual noise level, trajectory smoothness requirements, aircraft scenario, and trajectory maneuverability.

[0009] In one possible implementation, the core parameters include the number of wavelet decomposition layers, the type of wavelet basis functions, the threshold coefficients, and the number of sampling points in the local fitting window.

[0010] In one possible implementation, after performing inverse wavelet transform on the corrected low-frequency component and the denoised high-frequency component to obtain smooth trajectory data, the method further includes: Determine whether the deviation between the smoothed trajectory data and the trajectory data is greater than a preset threshold; If the deviation is determined to be greater than the first preset deviation, then the emergency handling mode is entered; In emergency handling mode, the wavelet decomposition layer is increased by one layer, and the high-frequency components of the newly added layer are averaged by taking multiple consecutive frames of data to obtain the average value; the average value is then processed by a hard threshold. If the deviation is determined to be less than the first preset deviation, the core parameters remain unchanged.

[0011] Secondly, embodiments of the present invention provide a trajectory smoothing device, the device comprising: The acquisition module is used to acquire the spatial position coordinates of the aircraft at various moments during flight to obtain trajectory data, which is represented as a three-dimensional discrete trajectory sequence. The decomposition module is used to perform discrete wavelet decomposition on the discrete trajectory sequence in each dimension to obtain low-frequency and high-frequency components. The noise reduction module is used to perform noise reduction processing on each layer of high-frequency components using an adaptive threshold to obtain the noise-reduced high-frequency components. The smoothing module is used to perform inverse wavelet transform on the corrected low-frequency component and the denoised high-frequency component to obtain smooth trajectory data.

[0012] Thirdly, embodiments of the present invention provide an embedded system, the embedded system including one or more processors; a memory; and one or more computer programs, wherein the one or more computer programs are stored in the memory, and the one or more computer programs include instructions that, when executed by the embedded system, cause the embedded system to perform the trajectory smoothing method as described in the first aspect or any possible implementation of the first aspect.

[0013] Fourthly, embodiments of the present invention provide a computer-readable storage medium comprising a stored program, wherein, when the program is executed, it controls the device on which the computer-readable storage medium is located to perform the trajectory smoothing method as described in the first aspect or any possible implementation thereof.

[0014] The technical solution provided in this invention, based on wavelet multi-scale decomposition, effectively separates high-frequency noise from the real motion components in the aircraft trajectory data. While achieving accurate denoising, it preserves as much key trajectory detail as possible, such as rapid maneuvers and sudden changes in the aircraft's trajectory, effectively avoiding the loss of detail and trajectory blurring caused by "overfitting" in traditional global fitting methods. Even for high-maneuvering segments in complex dynamic flight processes, it can still achieve high-fidelity trajectory reconstruction.

[0015] In this embodiment of the invention, core parameters are adaptively adjusted based on different scenarios to achieve simultaneous processing of multi-scale features such as global trends, local disturbances, and sudden anomalies. The denoising threshold is also adaptively adjusted based on different scenarios to strengthen or weaken noise suppression, thereby achieving precise suppression of various high-frequency interferences.

[0016] In this embodiment of the invention, the algorithm has a clear structure and moderate computational load, facilitating hardware acceleration and multi-threaded parallelism, thus meeting the stringent requirements for real-time trajectory data processing of aircraft. It can be directly integrated into the aircraft's flight control embedded system, supporting offline post-processing of batch trajectory data and providing a highly reliable foundation for engineering applications. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating a trajectory smoothing method provided in an embodiment of the present invention.

[0018] Figure 2 This is a schematic diagram of trajectory data processing provided in an embodiment of the present invention.

[0019] Figure 3 This is a schematic diagram of a trajectory smoothing device provided in an embodiment of the present invention.

[0020] Figure 4 This is a schematic diagram of an embedded system provided in an embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer and more understandable, the invention will be further described below in conjunction with the accompanying drawings and specific embodiments. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0022] Figure 1 This is a flowchart illustrating a trajectory smoothing method provided in an embodiment of the present invention, as shown below. Figure 1 As shown, the method includes: Step 101: Collect the spatial position coordinates of the aircraft at various moments during flight to obtain trajectory data, which is represented as a three-dimensional discrete trajectory sequence.

[0023] In this step, the trajectory data is represented as a discrete trajectory sequence in three dimensions: X, Y, and Z. Specifically, in the X dimension... In the Y dimension, In the Z dimension, .

[0024] Step 102: Perform discrete wavelet decomposition on the discrete trajectory sequence in each dimension to obtain low-frequency and high-frequency components.

[0025] In this step, the discrete trajectory sequence in each dimension is decomposed using J-level discrete wavelet decomposition to obtain low-frequency components (approximate components) and high-frequency components (detail components) at different scales, specifically a low-frequency component. and J high-frequency components .

[0026] Step 103: Use an adaptive threshold to denoise each high-frequency component to obtain the denoised high-frequency components.

[0027] In this embodiment of the invention, different threshold types are selected during the denoising process of high-frequency components to achieve noise processing under different noise scenarios. Threshold types include hard thresholding, soft thresholding, and a modified Garrote threshold. Hard thresholding is suitable for strong noise scenarios (such as areas with dense electromagnetic interference) and can quickly eliminate extreme noise. The processing logic of hard thresholding is: set to 0 when the amplitude is less than the adaptive threshold, and retain the original value when the amplitude is greater than or equal to the adaptive threshold. Soft thresholding is suitable for scenarios with rich trajectory details (such as aircraft takeoff and landing, maneuvers), prioritizing the preservation of trajectory details. The processing logic of soft thresholding is: set to 0 when the amplitude is less than the adaptive threshold, and retain the original value by linear attenuation when the amplitude is greater than or equal to the adaptive threshold. Modified Garrote thresholding is suitable for scenarios with mixed noise and details (such as airborne cruise + slight airflow interference), balancing noise suppression and detail preservation. The processing logic of modified Garrote thresholding is: set to 0 when the amplitude is less than the adaptive threshold, and retain the value by secondary attenuation when the amplitude is greater than or equal to the adaptive threshold.

[0028] In this embodiment of the invention, the soft threshold function is:

[0029] in, This represents the amplitude of the high-frequency component at point k in the j-th layer. This indicates an adaptive threshold.

[0030] In this embodiment of the invention, the noise standard deviation is estimated based on the median absolute deviation of the high-frequency components; a base threshold value is set based on the noise standard deviation, the sampling frequency of the trajectory data, and the number of sampling points; the adaptive threshold is the product of the threshold coefficient and the base threshold value. If the noise ratio is less than a first preset ratio, the threshold coefficient is lowered, and the adaptive threshold is lowered; if the noise ratio is greater than a second preset ratio, the threshold coefficient is raised, and the adaptive threshold is raised; the noise ratio is used to indicate the proportion of sampling points with amplitudes less than the base threshold value to the total number of sampling points.

[0031] For example, the first preset ratio is 30%, and the second preset ratio is 70%. If the noise ratio is less than 30%, it indicates that the high-frequency components contain a large amount of trajectory maneuvering details, such as aircraft turning and climbing. In this case, the threshold coefficient is lowered to 0.85 to reduce the adaptive threshold to 0.85 times the base threshold value, thereby reducing the noise suppression intensity and avoiding the accidental deletion of effective details. If the noise ratio is greater than 70%, it indicates that the high-frequency components are dominated by noise, such as high-frequency interference from sensors. In this case, the threshold coefficient is increased to 1.12 to increase the adaptive threshold to 1.12 times the base threshold value, thereby strengthening the noise suppression intensity.

[0032] The formulas for calculating the noise standard deviation and the median absolute deviation are as follows: σ≈MAD / 0.6745

[0033] Where σ represents the noise standard deviation and MAD represents the median absolute deviation.

[0034] The formula for calculating the base value of the threshold is:

[0035] in, σ represents the baseline threshold value, σ represents the noise standard deviation, and N represents the number of sampling points. Indicate the sampling frequency (e.g., 500Hz, 1kHz) to ensure that the noise estimation is adapted to the time resolution of the trajectory data, rather than relying on fixed coefficients of the vibration signal.

[0036] In the actual flight environment of an aircraft, Gaussian noise (such as sensor thermal noise) and impulse noise (such as sudden electromagnetic interference pulses) may coexist. The dominant noise type is determined by the kurtosis and peak factor of the high-frequency components. For example, when the kurtosis is >3 and the peak factor is >5, the dominant noise type is determined to be impulse noise; when the kurtosis is ≈3 and the peak factor is <3, the dominant noise type is determined to be Gaussian noise. For shallow high-frequency components, if the dominant noise type is impulse noise, hard thresholding is used for denoising; if the dominant noise type is Gaussian noise, soft thresholding is used for denoising; for deep high-frequency components, an improved Garrote thresholding method is used for denoising to obtain the denoised high-frequency components.

[0037] In this embodiment of the invention, the shallow high-frequency components refer to the first or second layer of high-frequency components, corresponding to high-frequency noise above 100Hz. When impulse noise dominates, a hard threshold is used for denoising, which can quickly eliminate sudden interference; when Gaussian noise dominates, a soft threshold is used for denoising, which can smoothly suppress noise. The deep high-frequency components refer to the third or fourth layer of high-frequency components, corresponding to mid-to-high frequency details in the 20-100Hz range. An improved Garrote threshold is used for denoising, which can suppress noise while preserving the amplitude variation trend of trajectory details.

[0038] In this embodiment of the invention, correlation analysis is performed on the high-frequency components after denoising between two adjacent layers (such as the high-frequency components of the second and third layers) to calculate the correlation coefficient. If the correlation coefficient is less than 0.3, it indicates that denoising may be excessive, that is, not only noise is removed but also some details are removed, resulting in poor correlation of details in the high-frequency components after denoising between adjacent layers. In this case, the adaptive threshold of the corresponding layer needs to be readjusted to ensure the consistency of noise suppression.

[0039] Step 104: Perform inverse wavelet transform on the corrected low-frequency components and the denoised high-frequency components to obtain smooth trajectory data.

[0040] In this embodiment of the invention, before step 104, the method further includes: using a low-order polynomial to locally fit the low-frequency component to obtain a trend fitting curve; using the 3σ criterion to determine whether the residual between the low-frequency component and the trend fitting curve is a low-frequency disturbance; if the residual is determined to be a low-frequency disturbance, then the low-frequency component is corrected using the trend fitting curve; and the time-frequency synchronization of the corrected low-frequency component and the denoised high-frequency component is verified.

[0041] Specifically, a low-order polynomial (such as a quadratic polynomial) is used to locally fit the low-frequency components. W consecutive sampling points are taken, and a fitting function is used to fit these sampling points, resulting in a trend curve. Here, W = sampling frequency / K, where K is between 10 and 20. For example, when the sampling frequency is 1 kHz and K is 10, W is 100. The fitting function is... Where t represents time. The residual between the low-frequency component and the trend fitting curve is expressed as... If the magnitude of the residual is greater than three times the standard deviation of the residual, the low-frequency component is replaced by a trend fitting curve to eliminate low-frequency interference such as airflow fluctuations and uneven ground.

[0042] In this embodiment of the invention, time-frequency synchronization verification is performed on the corrected low-frequency components and the denoised high-frequency components to ensure that their sampling times are completely aligned. Based on this, an inverse wavelet transform is performed to avoid distortion of the reconstructed smooth trajectory data caused by time-frequency deviations between low-frequency trends and high-frequency details. This is particularly suitable for high-speed maneuvering scenarios of aircraft (such as supersonic flight scenarios) and meets the requirements for trajectory continuity.

[0043] In this embodiment of the invention, the core parameters during trajectory smoothing include the number of wavelet decomposition levels, the type of wavelet basis functions, the threshold coefficient, and the number of sampling points in the local fitting window. Initial core parameters are determined based on the sampling frequency and average velocity. These initial core parameters are dynamically adjusted based on the actual noise level, trajectory smoothness requirements, aircraft scenario, and trajectory maneuverability, effectively suppressing multi-scale noise while preserving as much physical detail and maneuverability as possible in the trajectory. The number of wavelet decomposition levels determines the fineness of multi-scale processing, ranging from 2 to 6 levels, and is positively correlated with the frequency range of the trajectory data. For example, when the trajectory data contains components of 0.1-100Hz, the number of decomposition levels is set to 5. Wavelet basis function types include db4 (adapting to abrupt signals), sym8 (adapting to smooth signals), and coif5 (adapting to signals with high detail preservation requirements). The selection of the wavelet basis function type must match the dynamic characteristics of the trajectory. The threshold coefficient is used to adjust the base threshold value, ranging from 0.8 to 1.5, and reflects the noise suppression strength. When the threshold coefficient is less than 1, the noise suppression strength is reduced; when the threshold coefficient is greater than 1, the noise suppression strength is strengthened. The local fitting window is used to achieve trend fitting of low-frequency components. The number of sampling points in the local fitting window is expressed as sampling frequency / K, where K is between 10 and 20, reflecting the time granularity of trend fitting.

[0044] In this embodiment of the invention, the initial number of decomposition layers is determined based on the sampling frequency. For example, when the sampling frequency is 1 kHz, the number of layers is set to 5; when the sampling frequency is 500 kHz, the number of layers is set to 4; and when the sampling frequency is 200 kHz, the number of layers is set to 3, ensuring that the frequency resolution of the multi-scale decomposition matches the sampling density.

[0045] In this embodiment of the invention, the initial wavelet basis and initial threshold type are determined based on the average velocity. For high-dynamic scenarios, such as aerial flight scenarios (average velocity > 200 m / s), db4 and a soft threshold are selected; for low-dynamic scenarios, such as ground taxiing scenarios (average velocity < 30 m / s), sym8 and a hard threshold are selected.

[0046] During trajectory smoothing, the actual noise level is quantified by noise energy. The relationship between the core parameters and noise energy lies in the following: For high-noise scenarios (such as industrial interference areas), the number of decomposition layers is increased to more finely separate multi-scale noise; and a hard threshold is selected, with the threshold coefficient increased (e.g., from 1.0 to 1.5), and the local fitting window increased (e.g., from 100 points to 150 points) to enhance noise suppression. For low-noise scenarios (such as high-altitude clean electromagnetic environments), the number of decomposition layers is reduced, and a soft threshold is selected, with the threshold coefficient decreased (e.g., from 1.0 to 0.8), and the local fitting window decreased (e.g., from 100 points to 50 points) to prioritize the preservation of trajectory details.

[0047] The formula for calculating noise energy is: / N in, Represents noise energy. This represents the amplitude of the high-frequency component at point k in the j-th layer. For example, >0.5 At that time, it was determined to be a high noise level; <0.1 When the noise level is low, it is determined to be low noise level.

[0048] In this embodiment of the invention, the core coefficient is related not only to the actual noise level but also to the trend of noise level change. By monitoring the noise energy of each frame in real time, the trend of noise level change is reflected, and core parameter adjustment is triggered when the parameter adjustment conditions are met. The relationship between the core coefficient and the trend of noise level change is as follows: if the noise energy of the current frame is greater than 1.2 times that of the previous frame for three consecutive frames (i.e., the noise energy increases for three consecutive frames with an increase of more than 20%), it indicates noise enhancement, triggering core parameter adjustment; the wavelet decomposition layer is increased by 1, and the threshold coefficient is increased by 0.1. If the noise energy of the current frame is less than 70% of that of the previous frame for three consecutive frames (i.e., the noise energy decreases for three consecutive frames with a decrease of more than 30%), it indicates noise reduction, triggering core parameter adjustment; the wavelet decomposition layer is decreased by 1, and the threshold coefficient is decreased by 0.1.

[0049] It should be noted that both the number of wavelet decomposition layers and the threshold coefficient have upper and lower limits. For example, the upper limit for the number of wavelet decomposition layers is 6 to avoid excessive decomposition leading to a surge in computation; the lower limit is 2 layers to prevent severe loss of detail. The upper limit for the threshold coefficient is 1.5, and the lower limit is 0.8.

[0050] In this embodiment of the invention, the trajectory smoothness requirement is quantified by the trajectory curvature change rate. The relationship between the core parameter and the trajectory smoothness requirement is as follows: For scenarios with high smoothness requirements (such as the cruise phase of an aircraft or constant-speed gliding on the ground), the number of decomposition layers is reduced (e.g., 2-3 layers), a soft threshold or an improved Garrote threshold is selected, the threshold coefficient is lowered (e.g., 0.8-1.0), and the number of sampling points in the local fitting window is increased (e.g., 100-120 points) to avoid over-smoothing leading to trend distortion. For scenarios with low smoothness requirements (such as aerobatic maneuvers or emergency turns), the number of decomposition layers is increased (e.g., 4-5 layers), a hard threshold is selected, the threshold coefficient is increased (e.g., 1.2-1.4), and the number of sampling points in the local fitting window is reduced (e.g., 50-80 points) to suppress high-frequency noise during maneuvers.

[0051] The formula for calculating the rate of change of trajectory curvature is:

[0052] in, This represents the rate of change of the trajectory curvature. This represents the curvature difference between adjacent time points. This represents the time difference between adjacent moments. For example, When the speed is less than 0.1 rad / s, it is considered a high smoothness requirement; When the noise level is greater than 0.5 rad / s, it is considered a low smoothness requirement. In practical applications, the threshold for determining the noise level and the threshold for determining the smoothness requirement can be set based on actual needs, and this embodiment of the invention does not limit this.

[0053] In this embodiment of the invention, the relationship between the core parameters and the aircraft scenario lies in the fact that different aircraft scenarios have different trajectory and noise characteristics. Core parameters are selected for different trajectory and noise characteristics to achieve efficient denoising under different aircraft scenarios. For example, in an air cruise scenario, the trajectory is stable, and the noise is mainly Gaussian noise. The sym8 wavelet basis function and soft thresholding are selected, with the wavelet decomposition layer set to 3 layers, the threshold coefficient set to 0.9, and the number of sampling points in the local fitting window set to 100. As another example, in an air maneuver scenario, the trajectory has many abrupt changes, and noise and details are mixed. The db4 wavelet basis function and improved Garrote thresholding are selected, with the wavelet decomposition layer set to 5 layers, the threshold coefficient set to 1.2, and the number of sampling points in the local fitting window set to 60. As yet another example, in a ground taxiing scenario, the trajectory is affected by ground vibration and contains low-frequency disturbances. The coif5 wavelet basis function and a layered processing strategy using hard thresholding for shallow layers and soft thresholding for deep layers are selected, with the wavelet decomposition layer set to 4 layers, the threshold coefficient set to 1.1, and the number of sampling points in the local fitting window set to 120.

[0054] In this embodiment of the invention, the degree of trajectory maneuverability is quantified by the standard deviation of trajectory curvature. The formula for calculating the standard deviation of trajectory curvature is as follows:

[0055]

[0056] in, This represents the standard deviation of the trajectory curvature, and M represents the number of statistical frames, with a default of 5 consecutive frames of data. Indicates the first The curvature of the frame trajectory. This represents the mean of the trajectory curvature of frame M. The larger the value, the more drastic the trajectory curvature fluctuation, i.e., the enhanced maneuverability; The smaller the value, the smoother the trajectory curvature fluctuation, meaning the maneuverability is reduced.

[0057] The relationship between core parameters and trajectory maneuverability is as follows: If the standard deviation of trajectory curvature is greater than a first preset threshold (e.g., 0.3 rad), it indicates enhanced trajectory maneuverability, such as aircraft turning or climbing. This triggers core parameter adjustment, switching the threshold type to an improved Garrote threshold to balance noise suppression and maneuver detail preservation; and reducing the number of sampling points in the local fitting window (e.g., reducing by 20 points) to improve the temporal resolution of trend fitting and adapt to rapid maneuvers. If the standard deviation of trajectory curvature is less than a second preset threshold (e.g., 0.1 rad), it indicates trajectory stability, such as aircraft cruise or uniform ground gliding. This triggers parameter adjustment, switching the threshold type to a soft threshold to smoothly suppress noise and avoid excessive detail attenuation; and increasing the number of sampling points in the local fitting window (e.g., increasing by 20 points) to enhance the stability of the global trend. The number of sampling points in the local fitting window has an upper and lower limit. For example, the upper limit is 150 points, and the lower limit is 50 points.

[0058] In this embodiment of the invention, it is determined whether the deviation between the smooth trajectory data and the trajectory data is greater than a preset deviation threshold. If the deviation is greater than a first preset deviation, an emergency processing mode is entered. In the emergency processing mode, the wavelet decomposition layer is increased by one layer, and the high-frequency components of the newly added layer are averaged over multiple consecutive frames to obtain an average value. The average value is then processed using a hard threshold. If the deviation is less than a first preset deviation, the core parameters remain unchanged. If the anomaly resolution condition is met, the emergency processing mode is exited, and the original core parameters are returned to normal. For example, the anomaly resolution condition is that the deviation is less than a second preset deviation (e.g., 0.1m) for 5 consecutive frames.

[0059] The formula for calculating the deviation is as follows:

[0060] in, Indicates deviation, These represent the smooth trajectory data respectively. value, Value and value, Representing the trajectory data value, Value and value.

[0061] In this embodiment of the invention, the final output of smooth trajectory data is authentic and reliable, laying a solid data foundation for subsequent key technical aspects such as guidance and control, trajectory reconstruction, state estimation, target recognition and anomaly detection, thereby improving the safety of the aircraft and the reliability of engineering decisions.

[0062] In related technologies, trajectory smoothing relies heavily on prior models and noise characteristics. Methods such as Kalman filtering and Wiener filtering require accurate system dynamics models and noise statistical characteristics (e.g., state transition matrix, covariance, power spectral density). However, actual aircraft flight environments are complex and interference types are varied, making prior noise data difficult to obtain or prone to change over time, leading to limited filtering performance, parameter mismatch, or even failure. In this invention, noise is adaptively identified and processed in the multi-scale wavelet domain, eliminating the need for precise modeling or pre-estimation of aircraft dynamics models and noise statistical characteristics, significantly reducing reliance on system models and prior noise parameters. Compared to filter algorithms that depend on system models and parameter tuning, this method exhibits stronger environmental adaptability and robustness.

[0063] The technical solution provided in this invention, based on wavelet multi-scale decomposition, effectively separates high-frequency noise from the real motion components in the aircraft trajectory data. While achieving accurate denoising, it preserves as much key trajectory detail as possible, such as rapid maneuvers and sudden changes in the aircraft's trajectory, effectively avoiding the loss of detail and trajectory blurring caused by "overfitting" in traditional global fitting methods. Even for high-maneuvering segments in complex dynamic flight processes, it can still achieve high-fidelity trajectory reconstruction.

[0064] In this embodiment of the invention, core parameters are adaptively adjusted based on different scenarios to achieve simultaneous processing of multi-scale features such as global trends, local disturbances, and sudden anomalies. The denoising threshold is also adaptively adjusted based on different scenarios to strengthen or weaken noise suppression, thereby achieving precise suppression of various high-frequency interferences.

[0065] In this embodiment of the invention, the algorithm has a clear structure and moderate computational load, facilitating hardware acceleration and multi-threaded parallelism, thus meeting the stringent requirements for real-time trajectory data processing of aircraft. It can be directly integrated into the aircraft's flight control embedded system, supporting offline post-processing of batch trajectory data and providing a highly reliable foundation for engineering applications.

[0066] Figure 2 This is a schematic diagram of trajectory data processing provided in an embodiment of the present invention, such as... Figure 2 As shown, the orange origin represents the original sampling points, i.e., the trajectory data, represented as a discrete trajectory sequence in three dimensions: X, Y, and Z. The red solid line represents the wavelet-smoothed trajectory, and the green dashed line represents the ideal parabola. Noise exists in the original sampling points; the trajectory smoothing method described in the above embodiment is used to smooth the original sampling points, resulting in the wavelet-smoothed trajectory. The wavelet-smoothed trajectory retains the detailed features of the original sampling points while approximating the ideal parabola. In other words, the wavelet-smoothed trajectory achieves accurate noise reduction while preserving key trajectory details as much as possible, achieving high-fidelity trajectory reconstruction.

[0067] Figure 3 This is a schematic diagram of the structure of a trajectory smoothing device provided in an embodiment of the present invention, as shown below. Figure 3 As shown, the device includes an acquisition module 11, a decomposition module 12, a denoising module 13, and a smoothing module 14. The acquisition module 11 is used to acquire the spatial position coordinates of the aircraft at various moments during flight, obtaining trajectory data, which is represented as a three-dimensional discrete trajectory sequence. The decomposition module 12 is used to perform discrete wavelet decomposition on the discrete trajectory sequence in each dimension, obtaining low-frequency and high-frequency components. The denoising module 13 is used to apply an adaptive threshold to denoise each layer of high-frequency components, obtaining denoised high-frequency components. The smoothing module 14 is used to perform inverse wavelet transform on the corrected low-frequency components and the denoised high-frequency components, obtaining smoothed trajectory data.

[0068] In this embodiment of the invention, the denoising module 13 includes an estimation submodule, a setting submodule, a first adjustment submodule, and a second adjustment submodule. The estimation submodule is used to estimate the noise standard deviation based on the median absolute deviation of the high-frequency components. The setting submodule is used to set a base threshold value based on the noise standard deviation, the sampling frequency of the trajectory data, and the number of sampling points; the adaptive threshold is the product of a threshold coefficient and the base threshold value. The first adjustment submodule is used to lower the threshold coefficient and adjust the adaptive threshold if the noise ratio is less than a first preset ratio. The second adjustment submodule is used to raise the threshold coefficient and adjust the adaptive threshold if the noise ratio is greater than a second preset ratio; the noise ratio indicates the proportion of sampling points with amplitudes less than the base threshold value to the total number of sampling points.

[0069] In this embodiment of the invention, the denoising module 13 includes a determination submodule, a first denoising submodule, and a second denoising submodule. The determination submodule is used to determine the dominant noise type based on the kurtosis and peak factor of the high-frequency components. For shallow high-frequency components, if the determination submodule determines the dominant noise type to be impulse noise, the first denoising submodule is triggered to perform denoising processing using a hard threshold; if the determination submodule determines the dominant noise type to be Gaussian noise, the first denoising submodule is triggered to perform denoising processing using a soft threshold. The second denoising submodule is used to perform denoising processing on deep high-frequency components using an improved Garrote threshold to obtain denoised high-frequency components.

[0070] In this embodiment of the invention, the device further includes a fitting module, a first judgment module, a correction module, and a verification module. The fitting module is used to locally fit the low-frequency component using a low-order polynomial to obtain a trend fitting curve. The first judgment module is used to determine, using the 3σ criterion, whether the residual between the low-frequency component and the trend fitting curve is a low-frequency disturbance. If the first judgment module determines that the residual is a low-frequency disturbance, it triggers the correction module to correct the low-frequency component using the trend fitting curve. The verification module is used to perform time-frequency synchronization verification on the corrected low-frequency component and the denoised high-frequency component.

[0071] In this embodiment of the invention, the device further includes a determining module and an adjusting module. The determining module is used to determine initial core parameters based on the sampling frequency and average velocity; the adjusting module is used to dynamically adjust the initial core parameters based on the actual noise level, trajectory smoothness requirements, aircraft scenario, and trajectory maneuverability.

[0072] In this embodiment of the invention, the core parameters include the number of wavelet decomposition layers, the type of wavelet basis function, the threshold coefficient, and the number of sampling points in the local fitting window.

[0073] In this embodiment of the invention, the device further includes a second judgment module, an emergency module, and a holding module. The second judgment module is used to determine whether the deviation between the smoothed trajectory data and the trajectory data is greater than a preset threshold; if the second judgment module determines that the deviation is greater than a first preset deviation, the emergency module is triggered to enter an emergency processing mode; in the emergency processing mode, the wavelet decomposition layer is increased by one layer, and the high-frequency components of the newly added layer are averaged by taking multiple consecutive frames of data to obtain an average value; the average value is processed by a hard threshold; if the second judgment module determines that the deviation is less than the first preset deviation, the holding module is triggered to keep the core parameters unchanged.

[0074] The technical solution provided in this invention, based on wavelet multi-scale decomposition, effectively separates high-frequency noise from the real motion components in the aircraft trajectory data. While achieving accurate denoising, it preserves as much key trajectory detail as possible, such as rapid maneuvers and sudden changes in the aircraft's trajectory, effectively avoiding the loss of detail and trajectory blurring caused by "overfitting" in traditional global fitting methods. Even for high-maneuvering segments in complex dynamic flight processes, it can still achieve high-fidelity trajectory reconstruction.

[0075] In this embodiment of the invention, core parameters are adaptively adjusted based on different scenarios to achieve simultaneous processing of multi-scale features such as global trends, local disturbances, and sudden anomalies. The denoising threshold is also adaptively adjusted based on different scenarios to strengthen or weaken noise suppression, thereby achieving precise suppression of various high-frequency interferences.

[0076] In this embodiment of the invention, the algorithm has a clear structure and moderate computational load, facilitating hardware acceleration and multi-threaded parallelism, thus meeting the stringent requirements for real-time trajectory data processing of aircraft. It can be directly integrated into the aircraft's flight control embedded system, supporting offline post-processing of batch trajectory data and providing a highly reliable foundation for engineering applications.

[0077] This invention provides a computer-readable storage medium that includes a stored program. When the program runs, it controls the device where the computer-readable storage medium is located to execute the steps of the above-described trajectory smoothing method. For a detailed description, please refer to the embodiments of the above-described trajectory smoothing method.

[0078] Figure 4 A schematic diagram of an embedded system provided in an embodiment of the present invention, such as... Figure 4 As shown, the embedded system 3 of this embodiment includes: a processor 301, a memory 302, and a computer program 303 stored in the memory 302 and executable on the processor 301. When the processor 301 executes the computer program 303, it implements the steps in the various method embodiments described above. Alternatively, when the processor 301 executes the computer program 303, it implements the functions of each module / unit in the various device embodiments described above.

[0079] Embedded system 3 can be an electronic device such as a desktop computer, laptop, handheld computer, or cloud-based embedded system. Embedded system 3 may include, but is not limited to, processor 301 and memory 302. Those skilled in the art will understand that... Figure 4 This is merely an example of embedded system 3 and does not constitute a limitation on embedded system 3. It may include more or fewer components than shown, or different components.

[0080] The processor 301 can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0081] The memory 302 can be an internal storage unit of the embedded system 3, such as a hard disk or RAM in the embedded system 3. The memory 302 can also be an external storage device of the embedded system 3, such as a plug-in hard disk, SmartMedia Card (SMC), Secure Digital (SD) card, or Flash Card equipped on the embedded system 3. The memory 302 can also include both internal storage units and external storage devices of the embedded system 3. The memory 302 is used to store computer programs and other programs and data required by electronic devices.

[0082] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0083] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A trajectory smoothing method, characterized in that, The method includes: The spatial position coordinates of the aircraft at various moments during flight are collected to obtain trajectory data, which is represented as a three-dimensional discrete trajectory sequence. Discrete wavelet decomposition is performed on the discrete trajectory sequence in each dimension to obtain low-frequency and high-frequency components; An adaptive threshold is used to denoise each high-frequency component to obtain the denoised high-frequency components. Perform inverse wavelet transform on the corrected low-frequency component and the denoised high-frequency component to obtain smooth trajectory data; Before performing inverse wavelet transform on the corrected low-frequency components and the denoised high-frequency components to obtain smooth trajectory data, the method further includes: A low-order polynomial is used to locally fit the low-frequency components to obtain a trend fitting curve; The 3σ criterion is used to determine whether the residual between the low-frequency component and the trend fitting curve is a low-frequency disturbance. If the residual is determined to be a low-frequency disturbance, the low-frequency component is corrected using the trend fitting curve. The time-frequency synchronization of the corrected low-frequency component and the denoised high-frequency component is checked.

2. The method according to claim 1, characterized in that, The step of employing an adaptive threshold to denoise each layer of high-frequency components, resulting in denoised high-frequency components, includes: The noise standard deviation is estimated based on the median absolute deviation of the high-frequency components; Based on the noise standard deviation, the sampling frequency of the trajectory data, and the number of sampling points, a base threshold value is set; the adaptive threshold is the product of the threshold coefficient and the base threshold value. If the noise ratio is less than the first preset ratio, then the threshold coefficient is lowered, and the adaptive threshold is lowered. If the noise ratio is greater than the second preset ratio, then the threshold coefficient is increased to adjust the adaptive threshold. The noise ratio is used to indicate the proportion of sampling points whose amplitude is less than the threshold base value out of the total number of sampling points.

3. The method according to claim 1, characterized in that, The high-frequency components contain both Gaussian noise and impulse noise. An adaptive threshold is used to denoise each layer of high-frequency components, resulting in denoised high-frequency components, including: The dominant noise type is determined by the kurtosis and peak factor of the high-frequency components; For shallow high-frequency components, if the dominant noise type is impulse noise, hard thresholding is used for denoising; if the dominant noise type is Gaussian noise, soft thresholding is used for denoising. For deep high-frequency components, an improved Garrote threshold is used for denoising to obtain the denoised high-frequency components.

4. The method according to claim 1, characterized in that, Before performing discrete wavelet decomposition on the discrete trajectory sequence in each dimension, the following steps are also included: The initial core parameters are determined based on the sampling frequency and averaging speed. The initial core parameters are dynamically adjusted based on the actual noise level, trajectory smoothness requirements, aircraft scenario, and trajectory maneuverability.

5. The method according to claim 4, characterized in that, The core parameters include the number of wavelet decomposition layers, the type of wavelet basis function, the threshold coefficient, and the number of sampling points in the local fitting window. The local fitting window is used to achieve trend fitting of the low-frequency components. The number of sampling points in the local fitting window is expressed as sampling frequency / K, where K is 10-20, reflecting the time granularity of trend fitting.

6. The method according to claim 5, characterized in that, After performing inverse wavelet transform on the corrected low-frequency component and the denoised high-frequency component to obtain smooth trajectory data, the method further includes: Determine whether the deviation between the smoothed trajectory data and the trajectory data is greater than a preset threshold; If the deviation is determined to be greater than the first preset deviation, then the emergency handling mode is entered; In emergency handling mode, the wavelet decomposition layer is increased by one layer, and the high-frequency components of the newly added layer are averaged by taking multiple consecutive frames of data to obtain the average value; the average value is then processed by a hard threshold. If the deviation is determined to be less than the first preset deviation, the core parameters remain unchanged.

7. A trajectory smoothing device, characterized in that, The device includes: The acquisition module is used to acquire the spatial position coordinates of the aircraft at various moments during flight to obtain trajectory data, which is represented as a three-dimensional discrete trajectory sequence. The decomposition module is used to perform discrete wavelet decomposition on the discrete trajectory sequence in each dimension to obtain low-frequency and high-frequency components. The noise reduction module is used to perform noise reduction processing on each layer of high-frequency components using an adaptive threshold to obtain the noise-reduced high-frequency components. The smoothing module is used to perform inverse wavelet transform on the corrected low-frequency component and the denoised high-frequency component to obtain smooth trajectory data. The fitting module is used to locally fit the low-frequency components using a low-order polynomial to obtain a trend fitting curve. The first judgment module is used to determine, by means of the 3σ criterion, whether the residual between the low-frequency component and the trend fitting curve is a low-frequency disturbance. If the first judgment module determines that the residual is a low-frequency disturbance, it triggers the correction module to correct the low-frequency component through the trend fitting curve; The verification module is used to verify the time-frequency synchronization of the corrected low-frequency component and the denoised high-frequency component.

8. An embedded system, characterized in that, The embedded system includes one or more processors; a memory; and one or more computer programs, wherein the one or more computer programs are stored in the memory, and the one or more computer programs include instructions that, when executed by the embedded system, cause the embedded system to perform the trajectory smoothing method according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored program, wherein, when the program is executed, it controls the device on which the computer-readable storage medium is located to perform the trajectory smoothing method as described in any one of claims 1 to 6.

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