Badminton trajectory data correction method based on flight dynamics constraints

Abstract

The application discloses a badminton trajectory data correction method based on flight dynamics constraints, and particularly relates to the fields of trajectory analysis and data correction, and is used for solving the problem that in the prior art, the image centroid position is periodically deviated due to the influence of spin during the flight of a badminton, the existing trajectory correction method is difficult to distinguish the real flight trajectory from the spin-induced observation error, and the trajectory correction accuracy is insufficient; the original observation centroid position time sequence is obtained by collecting a badminton flight image sequence, a smooth reference trajectory is generated in combination with a flight dynamics model, and an observation residual is extracted, the spin change rule is identified according to the residual spectrum characteristics, the mapping relationship between the spin rate and the centroid deviation is established, the spin-induced centroid deviation error is predicted, and an augmented state space model is constructed to recursively correct the observed trajectory, so that the flight trajectory data from which the spin-induced periodic centroid deviation is removed is obtained.

Description

Technical Field

[0001] This invention relates to the field of trajectory analysis and data correction technology, and more specifically, to a method for correcting badminton trajectory data based on flight dynamics constraints. Background Technology

[0002] With the development of badminton training, competitive event analysis, and intelligent referee assistance technologies, badminton flight trajectory analysis technology based on high-speed visual acquisition has been widely applied in scenarios such as shot quality assessment, flight trajectory reconstruction, landing point determination, athlete tactical analysis, and intelligent training feedback. In practical applications, high-speed cameras are typically used to continuously acquire images of the badminton shuttlecock in flight. The positional changes of the shuttlecock in the continuous images are obtained through target detection, centroid localization, and other methods. Then, the flight trajectory, flight speed, and flight attitude are analyzed based on the continuous positional data.

[0003] However, due to the shuttlecock's structural characteristics—concentrated mass at the head, high-speed rotation of the feather skirt, and significant air resistance—it typically undergoes continuous spin during flight, with the feathers constantly changing their spread. This causes periodic changes in the shuttlecock's brightness distribution and outline shape in the image, resulting in a periodic shift in the centroid position obtained using visual positioning methods such as the grayscale centroid method relative to the true geometric center. Furthermore, as the flight speed gradually decreases, the spin speed also changes, making this shift exhibit a non-stationary characteristic that varies continuously with the flight stage.

[0004] Existing trajectory correction methods mostly focus on filtering and denoising, trajectory smoothing, or trajectory optimization based on flight dynamics constraints. They usually treat the aforementioned periodic offsets as random noise and find it difficult to effectively identify and compensate for periodic observation errors caused by badminton shuttlecock spin. As a result, the corrected trajectory still has local swaying, position offset, and flight parameter estimation errors, which affect the accuracy of subsequent flight trajectory analysis, velocity calculation, and motion performance evaluation. Summary of the Invention

[0005] To overcome the aforementioned deficiencies of the prior art, embodiments of the present invention provide a badminton trajectory data correction method based on flight dynamics constraints to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for correcting badminton shuttlecock trajectory data based on flight dynamics constraints includes the following steps: S1. Collect image sequences of badminton shuttlecock flight, extract the badminton shuttlecock region in the image frame by frame, and calculate the pixel coordinates using the gray-scale centroid method to generate the original observation centroid position time series. S2. Based on the aerodynamic drag coefficient and lift coefficient of badminton flight, establish the recursive relationship of particle flight dynamics. Using the original observed centroid position time series as input, perform forward prediction and backward smoothing to generate a smooth reference trajectory. Then, calculate the difference between the original observed centroid position time series and the smooth reference trajectory frame by frame to obtain the observation residual time series. S3. Apply a sliding time window to the observed residual time series and calculate the power spectral density. Extract the periodic components whose energy proportion exceeds the preset threshold and whose frequency decreases monotonically with time. Identify the instantaneous frequency curve and amplitude envelope curve of the periodic components. S4. Establish a mapping function between the badminton shuttlecock spin rate and the centroid offset vector, convert the instantaneous frequency curve into a spin rate decay curve, and use the spin rate decay curve and amplitude envelope curve as inputs to generate a centroid offset error prediction sequence that changes synchronously with the flight phase. S5. Update the true center of mass position state variables according to the recursive relationship of flight dynamics, update the spin error state variables according to the predicted sequence of center of mass offset error, and form the predicted observation values ​​by combining the true center of mass position state variables and the spin error state variables to construct an augmented state space model. S6. Input the original observed centroid position time series into the augmented state space model. Based on the measurement residual between the predicted observation and the original observed centroid position, recursively correct the augmented state vector to obtain the corrected centroid coordinates and generate flight trajectory data.

[0008] As a further aspect of the present invention, S1 specifically includes: For each frame of image, the gradient magnitude is calculated at multiple scales, and connected components with closed contours are extracted as candidate badminton shuttlecock regions. The badminton shuttlecock region of the current frame is determined based on the matching degree between the area and contour curvature features of the candidate badminton shuttlecock regions and the confirmed badminton shuttlecock regions of the previous frame. Subtract the average gray value of pixels in the annular neighborhood that extends outward from the bounding rectangle of the determined badminton area from the gray value of the pixels in the determined badminton area as the background compensation term. Perform square weighting on the compensated gray value and calculate the weighted gray centroid coordinates as the pixel coordinates of the current frame. Repeat the above process frame by frame, and arrange the pixel coordinates obtained from each frame in chronological order to generate the original observation centroid position time series.

[0009] As a further aspect of the present invention, S2 specifically includes: The aerodynamic drag coefficient and lift coefficient of badminton shuttlecock flight are obtained, and a recursive relationship of the dynamics of point mass flight is constructed based on the aerodynamic drag coefficient and lift coefficient. The recursive relationship uses the current position, velocity and acceleration of the center of mass as state variables, and air density, shuttlecock mass and reference area as recursive constants. Using the first frame of the original observed centroid position time series as the initial state, the recursive relation is used to calculate the predicted centroid position frame by frame along the increasing time direction to generate the forward predicted trajectory; using the last frame of the original observed centroid position time series as the final state, the recursive relation is used to calculate the estimated centroid position frame by frame along the decreasing time direction to generate the backward smoothed trajectory. The forward predicted trajectory position and the backward smoothed trajectory position corresponding to the same frame are fused, and the fusion result is used as the smoothed reference trajectory position; the centroid position of each frame in the original observed centroid position time series is subtracted from the smoothed reference trajectory position, and the resulting difference sequence is used as the observed residual time series.

[0010] As a further aspect of the present invention, S3 specifically includes: Set the window length and step size parameters of the sliding time window. The window length parameter is greater than the estimated period of the badminton shuttlecock spin motion. The observed residual time series is segmented from the starting frame according to the step size parameter to obtain a set of time window residual segments. For each time window residual segment, the power spectral density is calculated, and the frequency corresponding to the maximum peak of the power spectral density is found as the dominant frequency of the current time window. The ratio of the peak energy corresponding to the dominant frequency to the total energy of the entire frequency band is calculated as the energy proportion of the current time window. Candidate frequency segments with energy proportions exceeding a preset threshold and dominant frequencies decreasing in time order are selected from the dominant frequency sequences corresponding to adjacent time windows. The center frequency of the time window corresponding to each candidate frequency segment is linearly interpolated to generate a periodic component frequency decay trajectory consistent with the length of the observed residual time series. Using the frequency decay trajectory of the periodic component as the center frequency, bandpass filtering is performed frame by frame on the observed residual time series. The instantaneous frequency curve of the periodic component is calculated based on the time interval between adjacent zero crossings in the filtered time series signal. At the same time, Hilbert transform is performed on the filtered time series signal, and the magnitude of the complex envelope is used as the amplitude envelope curve of the periodic component.

[0011] As a further aspect of the present invention, S4 specifically includes: Images of badminton shuttlecocks at different spin rates were acquired. The gray-scale centroid coordinates and the true geometric center coordinates of each frame were calculated. The difference between the two coordinates was used as the centroid offset vector corresponding to the spin rate. After multiple sets of spin rate discrete sampling, the mapping function between the spin rate and the centroid offset vector was obtained by fitting. The frequency value of each frame in the instantaneous frequency curve is converted into the spin rate of the corresponding frame according to the preset proportional coefficient between frequency and spin rate, and the spin rate decay curve is calculated frame by frame. The amplitude envelope curve is normalized to obtain the amplitude modulation coefficients corresponding to each frame. The spin rate value of each frame in the spin rate decay curve is substituted into the mapping function to obtain the reference centroid offset vector corresponding to that frame. The reference centroid offset vector is scaled by the amplitude modulation coefficient of the same frame to obtain the centroid offset error prediction vector of that frame. After frame-by-frame calculation, a centroid offset error prediction sequence that changes synchronously with the flight phase is generated.

[0012] As a further aspect of the present invention, S5 specifically includes: The true centroid position state variables are the horizontal coordinates, vertical coordinates, horizontal velocity, and vertical velocity of the badminton shuttlecock in the image pixel coordinate system, and the spin error state variables are the horizontal and vertical deviation components of the centroid offset error prediction sequence in the current frame. The true center of mass position state variable and the spin error state variable are concatenated end to end to form a six-dimensional augmented state vector; the true center of mass position state variable is updated frame by frame according to the recursive relationship of the particle flight dynamics, and the spin error state variable is updated frame by frame according to the difference between the predicted values ​​of two adjacent frames in the center of mass offset error prediction sequence. The augmented state space model is constructed by adding the horizontal coordinate of the true centroid position state variable to the horizontal deviation component of the spin error state variable, and adding the vertical coordinate to the vertical deviation component to form the predicted observation value.

[0013] As a further aspect of the present invention, S6 specifically includes: The augmented state vector is initialized with the original centroid position coordinates of the first frame, the initial velocity calculated based on the continuous observation frames, and the predicted centroid offset error value of the first frame. The estimated error covariance matrix is ​​initialized as a diagonal matrix. Starting from the second frame, the posterior estimate of the augmented state vector of the previous frame is substituted into the augmented state space model to obtain the prior estimate of the augmented state vector of the current frame, and the estimated error covariance matrix is ​​updated. Based on the measurement residual between the original observed centroid position and the predicted observed value in the current frame, the gain matrix is ​​calculated using the estimated error covariance matrix and the observation Jacobian matrix. The prior estimate of the augmented state vector is then corrected to obtain the posterior estimate of the augmented state vector in the current frame. Extract the horizontal and vertical coordinates of the true centroid position state variable from the posterior estimate of the augmented state vector of the current frame as the corrected centroid coordinates. After executing frame by frame, arrange the flight trajectory data in frame order and output it.

[0014] The technical effects and advantages of the badminton trajectory data correction method based on flight dynamics constraints of this invention are as follows: This invention generates a smooth reference trajectory by establishing a badminton shuttlecock flight dynamics constraint model and extracting observation residuals from the original observed trajectory. While preserving the true flight motion characteristics, it effectively separates the periodic observation error caused by the shuttlecock's spin, avoiding the uniform filtering of spin error as random noise and improving the targeted nature of trajectory correction. Simultaneously, it identifies the spin variation pattern using the spectral characteristics of the observation residuals and, combined with a pre-established mapping relationship between spin rate and center-of-mass shift, predicts spin-induced center-of-mass shifts. This allows for dynamic compensation of periodic shifts throughout the flight phase, improving the consistency and stability of trajectory corrections across different flight stages.

[0015] This invention also constructs an augmented state-space model that simultaneously includes the actual motion state and the spin error state, and synchronously corrects the flight state and spin error during the recursive estimation process. This allows the trajectory correction process to take into account both the continuity of flight dynamics and the consistency of visual observation, reduces the impact of the periodic oscillation of the center of mass on the accuracy of trajectory reconstruction, and improves the continuity and stability of badminton flight trajectory data. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of a badminton trajectory data correction method based on flight dynamics constraints according to the present invention. Detailed Implementation

[0017] 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 embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0018] Example 1 Figure 1 This invention presents a method for correcting badminton trajectory data based on flight dynamics constraints, which includes the following steps: S1. Collect image sequences of badminton shuttlecock flight, extract the badminton shuttlecock region in the image frame by frame, and calculate the pixel coordinates using the gray-scale centroid method to generate the original observation centroid position time series. S2. Based on the aerodynamic drag coefficient and lift coefficient of badminton flight, establish the recursive relationship of particle flight dynamics. Using the original observed centroid position time series as input, perform forward prediction and backward smoothing to generate a smooth reference trajectory. Then, calculate the difference between the original observed centroid position time series and the smooth reference trajectory frame by frame to obtain the observation residual time series. S3. Apply a sliding time window to the observed residual time series and calculate the power spectral density. Extract the periodic components whose energy proportion exceeds the preset threshold and whose frequency decreases monotonically with time. Identify the instantaneous frequency curve and amplitude envelope curve of the periodic components. S4. Establish a mapping function between the badminton shuttlecock spin rate and the centroid offset vector, convert the instantaneous frequency curve into a spin rate decay curve, and use the spin rate decay curve and amplitude envelope curve as inputs to generate a centroid offset error prediction sequence that changes synchronously with the flight phase. S5. Update the true center of mass position state variables according to the recursive relationship of flight dynamics, update the spin error state variables according to the predicted sequence of center of mass offset error, and form the predicted observation values ​​by combining the true center of mass position state variables and the spin error state variables to construct an augmented state space model. S6. Input the original observed centroid position time series into the augmented state space model. Based on the measurement residual between the predicted observation and the original observed centroid position, recursively correct the augmented state vector to obtain the corrected centroid coordinates and generate flight trajectory data.

[0019] In step S1, acquiring an image sequence of badminton shuttlecock flight, extracting the badminton shuttlecock region from the image frame by frame, and calculating pixel coordinates using the gray-scale centroid method to generate the original observed centroid position time series specifically includes: The input single-frame image is converted from its original color space to grayscale space to generate a single-channel grayscale image. Then, a Gaussian pyramid is constructed, consisting of three smooth layers with progressively increasing Gaussian kernel parameters: the bottom layer has a kernel value of 1.0, the middle layer has a value of 2.0, and the top layer has a value of 4.0. For each layer of the Gaussian pyramid, the Sobel gradient is calculated in both the horizontal and vertical directions. The square root of the sum of the squares of the gradients in both directions is used to obtain the gradient magnitude map for that layer. The three gradient magnitude maps are fused across scales by taking the maximum value pixel-by-pixel to generate a multi-scale gradient magnitude map. On the fused multi-scale gradient magnitude map, a connected component extraction algorithm is used to traverse all pixels. Adjacent pixels with gradient magnitudes exceeding a preset edge threshold are grouped into the same connected component. The edge threshold is automatically determined based on the 95th percentile of the gradient magnitude histogram of the entire image. An ellipse is fitted to each connected component, and the ratio of the major and minor axes and the fitting residual are calculated. Connected components with a major and minor axis ratio falling between 0.6 and 1.0 and a fitting residual below the preset ellipse fitting threshold are selected as candidate badminton shuttlecock regions. The preset ellipse fitting threshold is set to the upper limit of the average distance from the pixel point in the connected region to the boundary of the fitted ellipse.

[0020] The area values ​​and contour curvature sequences of candidate badminton shuttlecock regions are extracted. The area values ​​are obtained by counting the total number of pixels in the connected components, and the contour curvature sequences are obtained by calculating the curvature values ​​of each point on the contour. The area difference ratio of each candidate badminton shuttlecock region in the current frame is calculated with the area of ​​the confirmed badminton shuttlecock region in the previous frame, and the shape context distance between the contour curvature sequences of the two regions is also calculated. The area difference ratio and shape context distance are weighted and summed according to preset weight coefficients of 0.4 and 0.6, respectively, to obtain the matching error. The candidate region with the smallest matching error is selected as the badminton shuttlecock region of the current frame. If the minimum matching error still exceeds the preset matching threshold, it is determined that there is occlusion in the current frame, and the position of the confirmed badminton shuttlecock region in the previous frame is used as the result of optical flow prediction. The preset matching threshold is determined by statistically analyzing the matching error distribution of correctly matched frames and non-matched frames in the training set.

[0021] Calculate the circumscribed rectangle of the badminton shuttlecock region in the current frame. Shift the four boundaries of the circumscribed rectangle outwards by a preset pixel width to form an extended rectangle. The preset pixel width is 1 / 10 of the shorter side length of the circumscribed rectangle. Subtract the original circumscribed rectangle from the extended rectangle to obtain a circular neighborhood. Calculate the arithmetic mean of the grayscale values ​​of all pixels within the circular neighborhood as the background grayscale mean of the frame. Iterate through each pixel within the badminton shuttlecock region, subtracting the background grayscale mean from its original grayscale value to obtain the compensated grayscale value. Set the grayscale value of pixels with a value less than 0 in the compensated grayscale value to zero. After the above compensation process, perform a squared weighted average on the compensated grayscale values. Calculate the square of the compensated grayscale value pixel by pixel, and use this squared value as a weight to perform a weighted average of the pixel coordinates of all pixels within the badminton shuttlecock region. Specifically, the horizontal coordinate of each pixel is multiplied by the square of its compensated grayscale value and summed, then divided by the sum of the squares of all compensated grayscale values ​​to obtain the weighted horizontal centroid coordinates. Similarly, the vertical coordinate of each pixel is multiplied by the square of its compensated grayscale value and summed, then divided by the sum of the squares of all compensated grayscale values ​​to obtain the weighted vertical centroid coordinates. These horizontal and vertical centroid coordinates together constitute the pixel coordinates of the current frame. This background compensation and squared-weighted centroid calculation process is repeated frame by frame, and the pixel coordinates obtained from each frame are arranged sequentially according to the image acquisition time to generate the original observed centroid position time series.

[0022] In S2, a recursive relationship of particle flight dynamics is established based on the aerodynamic drag coefficient and lift coefficient of badminton flight. The original observed centroid position time series is used as input to perform forward prediction and backward smoothing to generate a smooth reference trajectory. The original observed centroid position time series and the smooth reference trajectory are then compared frame by frame to obtain the observed residual time series.

[0023] The system retrieves corresponding aerodynamic parameter entries from a pre-set aerodynamic parameter database. These entries were established through multiple aerodynamic measurement experiments conducted in a wind tunnel on various brands and models of badminton shuttlecocks under different wind speeds. Each experiment recorded the incoming airflow velocity, shuttlecock attitude angle, and corresponding aerodynamic drag and lift coefficients, which were stored in a query table for retrieval. The query uses the brand / model as the primary index key and the tournament level as the secondary index key for matching. The extracted aerodynamic drag and lift coefficients are stored in dimensionless form. A recursive relationship for point mass flight dynamics is constructed based on the aerodynamic drag and lift coefficients. This recursive relationship uses the current center of mass position coordinates, velocity components, and acceleration components as state variables, and air density, shuttlecock mass, and reference area as recursive constants. Air density is taken from a standard atmospheric density table based on the altitude and temperature of the competition venue, while the shuttlecock mass and reference area use standard values ​​for competition shuttlecocks. The recurrence relation is constructed according to the classical external ballistics equations for a point mass, including aerodynamic drag and lift terms. The aerodynamic drag term is proportional to the square of the current center-of-mass velocity and its direction is opposite to the velocity direction. The lift term is perpendicular to the velocity direction and its direction points towards the shuttlecock's skirt. An example of a vector form recurrence equation is as follows: ; For the quality of badminton, Let the velocity vector of the center of mass of the badminton shuttlecock at the current moment be... For air density, For badminton shuttlecock reference area, The aerodynamic drag coefficient, The lift coefficient, It is a unit direction vector that is perpendicular to the velocity vector and points towards the side of the badminton shuttlecock.

[0024] Using the first frame observation of the original centroid position time series as the initial state for recursion, the initial centroid velocity is determined by the ratio of the difference between the centroid positions observed in the first and second frames to the frame interval time. Frame by frame along the increasing time direction, the current frame state is substituted into the recursive relation to calculate the predicted centroid position and predicted centroid velocity for the next frame, generating a forward prediction trajectory from the first frame to the last frame.

[0025] The centroid position coordinates of the last frame in the original observed centroid position time series are extracted as the endpoint of the backward recursion. The endpoint velocity is determined by inverting the ratio of the difference between the observed centroid positions of the last frame and the penultimate frame to the frame interval. The velocity directions of the aerodynamic drag and lift terms in the recursive relation are reversed, so that they act on the motion estimation in the decreasing time direction. Starting from the last frame, the estimated centroid position and estimated velocity of the previous frame are calculated backward by substituting them into the recursive relation frame by frame in the decreasing frame order until the first frame is reached, resulting in a complete backward smoothed trajectory. The forward predicted trajectory position and the backward smoothed trajectory position corresponding to the same frame are weighted and fused to generate the smoothed reference trajectory position for that frame. The weights of the weighted fusion are determined according to the relative position of the frame in the original observed centroid position time series; the closer the frame order is to the first frame, the greater the weight of the forward predicted trajectory position; the closer the frame order is to the last frame, the greater the weight of the backward smoothed trajectory position. The weight allocation adopts a linear gradient method. In the first frame, the forward weight is 1 and the backward weight is 0. In the last frame, the forward weight is 0 and the backward weight is 1. The weights in the intermediate frames are linearly interpolated according to the frame order. The fusion result is the horizontal and vertical coordinates of the smooth reference trajectory position of the frame in the pixel coordinate system.

[0026] For each frame, the horizontal coordinate of the original observed centroid position is subtracted from the horizontal coordinate of the smoothed reference trajectory position to obtain the horizontal residual component of that frame; the vertical coordinate of the original observed centroid position is subtracted from the vertical coordinate of the smoothed reference trajectory position to obtain the vertical residual component of that frame. The horizontal and vertical residual components together constitute the observation residual of that frame. These subtraction operations are performed sequentially from the first frame to the last frame according to the frame order, generating an observation residual time series of the same length as the original observed centroid position time series. The residual value of each frame in this observation residual time series contains two dimensions: the horizontal residual component and the vertical residual component, reflecting the degree of deviation of the original observed centroid position from the smoothed reference trajectory in the horizontal and vertical directions, respectively.

[0027] In step S3, a sliding time window is applied to the observed residual time series and the power spectral density is calculated. Periodic components whose energy proportion exceeds a preset threshold and whose frequency decreases monotonically with time are extracted, and the instantaneous frequency curve and amplitude envelope curve of the periodic components are identified.

[0028] The estimated period is obtained by attaching markers to a badminton shuttlecock and using high-speed photography to record the shuttlecock's flight process under multiple sets of standard smashes. The rotation angle of the markers around the shuttlecock's center of mass is tracked from the image sequence, and the initial spin frequency of each flight process is calculated. The average of multiple initial spin frequencies is taken as the typical spin frequency of the shuttlecock. The reciprocal of the typical spin frequency is the estimated period of the spin motion. For example, the lower limit of the typical spin frequency is 8 revolutions per second, corresponding to a period of approximately 0.125 seconds. The window length parameter is set to twice the estimated period as the lower limit, meaning the number of frames corresponding to the window length must at least cover the product of the image acquisition frame rate and 0.25 seconds. The step size parameter is set to 1 / 4 of the window length parameter to ensure the overlap between adjacent time windows. Starting from the initial frame, the observed residual time series is segmented segment by segment, using the window length as the cut length and the step size as the sliding interval, to obtain a set of time window residual segments. The first time window residual segment covers the residual data from the starting frame to the starting frame plus the window length minus one frame. The second time window residual segment covers the residual data from the starting frame plus the step size frame to the starting frame plus the step size plus the window length minus one frame, and so on, until the truncation window exceeds the last frame of the observed residual time series, at which point truncation stops. Each time window residual segment contains the horizontal and vertical residual components of each frame within the corresponding frame number range. The square root of the sum of the squares of the horizontal and vertical residual components is taken to obtain the resultant displacement residual sequence of that time window residual segment, which is used for subsequent power spectral density calculation.

[0029] For the combined shift residual sequence of a single time window residual segment, a Hanning window function is applied to suppress spectral leakage. The length of the Hanning window function is equal to the number of frames contained in the time window residual segment. The windowed sequence is transformed to the frequency domain using a Fast Fourier Transform (FFT). The square of the amplitude of each frequency component in the transform result is divided by the frequency resolution to obtain the power spectral density sequence of the time window residual segment. Peak values ​​are found in the power spectral density sequence, and the frequencies corresponding to the peak values ​​are determined as the dominant frequencies. The integral value of the peak value under the power spectral density curve is recorded as the peak energy of the dominant frequency. The total energy of the power spectral density sequence of the time window residual segment in the entire frequency band from zero frequency to the Nyquist frequency range is calculated. The total energy is obtained by performing a trapezoidal integral on the values ​​of the power spectral density sequence at all frequency points. The peak energy of the dominant frequency is divided by the total energy of the entire frequency band to obtain the energy proportion of the time window. The above calculation is repeated for all time window residual segments to obtain the dominant frequency and energy proportion corresponding to each time window. The dominant frequencies of each time window are arranged according to the frame number of the center frame of the time window to form the dominant frequency sequence. Time windows with an energy percentage exceeding a preset threshold of 0.3 are selected from the dominant frequency sequence. This threshold is determined by statistically analyzing the power distribution of badminton spin signals and non-spin noise signals. Within the selected time windows, continuous segments where the dominant frequency value monotonically decreases with increasing frame number are identified, and each continuous segment is marked as a candidate frequency segment. Linear interpolation is performed on the frequency values ​​corresponding to the center frames of each time window within each candidate frequency segment, with an interpolation density of one frequency value per frame, generating a periodic component frequency decay trajectory consistent with the length of the observed residual time series.

[0030] Using the frequency decay trajectory of the periodic component as the center frequency, bandpass filtering is performed frame-by-frame on the observed residual time series. The bandpass filter is an infinite impulse response Butterworth type, with a filter order of 4. The lower passband cutoff frequency is set to 0.8 times the center frequency, and the upper passband cutoff frequency is set to 1.2 times the center frequency. The stopband attenuation is set to 40 dB relative to the passband gain. Since the center frequency changes with the frame sequence, a separate bandpass filter coefficient is designed for each frame. The design method uses bilinear transform to map the analog Butterworth filter to the digital domain. The observed residual time series is input frame-by-frame into the corresponding frame number's bandpass filter, and the filtered time series signal is output. The filtered time series signal is in sine wave form. The time interval between adjacent positive zero-crossing points is extracted. A positive zero-crossing point is defined as the time point corresponding to the signal value changing from negative to positive. The reciprocal of the time interval between adjacent positive zero-crossing points is the instantaneous frequency of that period. The instantaneous frequency values ​​of each period are arranged according to the corresponding frame number to obtain the instantaneous frequency curve of the periodic component. Simultaneously, a Hilbert transform is performed on the filtered time-series signal. The filtered signal is used as the real part, and the Hilbert transform result as the imaginary part to construct an analytic signal. The magnitude of the analytic signal is the envelope amplitude of the signal in each frame. Arranging this envelope amplitude sequence by frame number yields the amplitude envelope curve of the periodic component. The instantaneous frequency curve and the amplitude envelope curve together describe the time-frequency characteristics of the spin-induced periodic component in the observation residual.

[0031] In step S4, a mapping function between the badminton shuttlecock spin rate and the centroid offset vector is established, the instantaneous frequency curve is converted into a spin rate decay curve, and the centroid offset error prediction sequence that changes synchronously with the flight phase is generated using the spin rate decay curve and the amplitude envelope curve as input.

[0032] A calibration device was built in a controllable wind tunnel. The incoming wind speed was set to 15 meters per second, corresponding to the typical speed of a badminton shuttlecock in the mid-flight phase, with the incoming wind direction parallel to the shuttlecock's longitudinal axis, simulating the longitudinal blowing conditions during shuttlecock flight. A high-speed photography device was set up outside the wind tunnel observation window, with the shuttlecock's skirt facing directly in front of the device during shooting, ensuring the image plane was parallel to the shuttlecock's cross-section. At each spin rate setting, 100 consecutive frames were captured, including images after the shuttlecock's spin stabilized. For each frame at each spin rate setting, the shuttlecock's head contour was detected using Hough circle transform and a circle was fitted. The coordinates of the center of this fitted circle were used as the coordinates of the true geometric center. The difference between the gray-level centroid coordinates and the true geometric center coordinates within the same frame was calculated in the horizontal and vertical directions to obtain the centroid offset vector for that frame. The mean of the horizontal and vertical components of the centroid offset vector for each of the 100 frames at that spin rate setting were then used as the centroid offset vector corresponding to that spin rate. The centroid offset vectors, with spin rates ranging from 0 to 30 revolutions per second (16 increments), are arranged in ascending order of spin rate. A cubic polynomial is used to fit the relationship between the horizontal offset component and the spin rate, and the same cubic polynomial is used to fit the relationship between the vertical offset component and the spin rate. The two fitted polynomial functions together constitute the mapping function between the spin rate and the centroid offset vector, and are pre-stored. Then, the frequency values ​​of each frame in the instantaneous frequency curve are converted to the corresponding frame's spin rate. A preset scaling factor of 1 is used in the conversion, meaning the frequency of the spin motion and the spin rate are numerically equal. The frequency values ​​of each frame in the instantaneous frequency curve are directly assigned to the corresponding frame's spin rate, resulting in the calculated spin rate decay curve.

[0033] The amplitude values ​​of all frames in the amplitude envelope curve are iterated to find the maximum amplitude. The amplitude value of each frame is divided by this maximum amplitude, and the quotient is the amplitude modulation coefficient for that frame. The amplitude modulation coefficient ranges from 0 to 1. The maximum amplitude occurs in the early stage of badminton flight when the spin is strongest and the amplitude of the periodic residual component is most significant. As the spin rate decays, the amplitude modulation coefficient gradually decreases along the frame sequence. Substituting the spin rate value of each frame in the spin rate decay curve into the mapping function, the horizontal and vertical components of the reference centroid offset vector for that frame are obtained by calculating using the cubic fitting polynomials of the horizontal and vertical offset components, respectively. The reference centroid offset vector is scaled using the amplitude modulation coefficient of the same frame, i.e., the horizontal component of the reference centroid offset vector is multiplied by the amplitude modulation coefficient of that frame to obtain the horizontal component of the centroid offset error prediction vector for that frame, and the vertical component of the reference centroid offset vector is multiplied by the amplitude modulation coefficient of that frame to obtain the vertical component of the centroid offset error prediction vector for that frame. The horizontal and vertical components together constitute the centroid offset error prediction vector for this frame.

[0034] The steps described above—calculating the reference offset vector by substituting it into the mapping function and scaling it with the amplitude modulation coefficient—are performed frame by frame. Each frame generates a centroid offset error prediction vector. The centroid offset error prediction vectors of all frames are arranged in frame order, generating a centroid offset error prediction sequence that changes synchronously with the flight phase. The centroid offset error prediction vector for each frame in this prediction sequence is directly related to the instantaneous amplitude of the badminton shuttlecock's spin rate and periodic residual in the current frame. The higher the spin rate and the larger the amplitude modulation coefficient, the larger the amplitude of the centroid offset error prediction vector. When the spin rate decays to near zero, the amplitude of the centroid offset error prediction vector also approaches zero.

[0035] In step S5, the true centroid position state variable is updated based on the recursive relationship of flight dynamics, the spin error state variable is updated based on the centroid offset error prediction sequence, and the predicted observation value is formed by the true centroid position state variable and the spin error state variable to construct an augmented state space model.

[0036] The true centroid position state variable and the spin error state variable are defined and augmented and concatenated. The true centroid position state variable contains four components: the horizontal coordinate, vertical coordinate, horizontal velocity, and vertical velocity of the badminton shuttlecock in the image pixel coordinate system. The horizontal and vertical coordinates are in pixels, and the horizontal and vertical velocities are in pixels per frame. The spin error state variable contains two components: the horizontal deviation component and the vertical deviation component of the centroid offset error prediction sequence in the current frame. These two components are the horizontal and vertical component values ​​of the generated centroid offset error prediction vector in the same frame. The true centroid position state variable and the spin error state variable are concatenated end-to-end in a specified order: horizontal coordinate, vertical coordinate, horizontal velocity, vertical velocity, horizontal deviation component, and vertical deviation component, forming a six-dimensional augmented state vector. This six-dimensional augmented state vector contains the above six components in each frame, and the value of each component in the current frame collectively represents the joint state of the badminton shuttlecock's motion and the observation deviation in that frame. The splicing operation is performed in memory as a vector append, with the augmented state vector of each frame occupying contiguous storage space. Subsequent state prediction and measurement updates use this six-dimensional vector as the basic operation unit.

[0037] The true center-of-mass position state variable is updated frame-by-frame based on the recursive relation of particle flight dynamics, and the spin error state variable is updated frame-by-frame based on the difference between the predicted values ​​of two adjacent frames in the center-of-mass offset error prediction sequence. An observation relationship for the augmented state space model is then constructed. The update of the true center-of-mass position state variable uses the constructed recursive relation of particle flight dynamics, which takes air density, sphere mass, and reference area as constants. The four components of the augmented state vector in the current frame—horizontal coordinate, vertical coordinate, horizontal velocity, and vertical velocity—are used as inputs to calculate the predicted value of the true center-of-mass position state variable for the next frame. The update of the spin error state variable uses a deterministic incremental approach. The difference between the horizontal deviation component of the next frame and the current frame in the center-of-mass offset error prediction sequence is extracted as the horizontal deviation increment, and the difference between the vertical deviation component of the next frame and the current frame is extracted as the vertical deviation increment. The horizontal deviation component in the augmented state vector of the current frame is added to the horizontal deviation increment, and the vertical deviation component is added to the vertical deviation increment to obtain the predicted value of the spin error state variable for the next frame. These two sets of updates together constitute the state transition relationship of the augmented state space model. The observation relationship is constructed as follows: the horizontal coordinates of the true centroid position state variable in the augmented state vector of the current frame are added to the corresponding horizontal deviation components of the spin error state variable to obtain the horizontal coordinates of the predicted observation; the vertical coordinates of the true centroid position state variable are added to the corresponding vertical deviation components of the spin error state variable to obtain the vertical coordinates of the predicted observation. The predicted observation represents the position of the badminton shuttlecock's centroid that should be observed in the image under the current state estimation, considering the spin-induced centroid shift. The state transition relationship and the observation relationship together constitute a complete augmented state space model, used for recursive state estimation.

[0038] In step S6, the original observed centroid position time series is input into the augmented state space model. Based on the measurement residual between the predicted observation and the original observed centroid position, the augmented state vector is recursively corrected to obtain the corrected centroid coordinates and generate flight trajectory data.

[0039] The horizontal and vertical coordinates of the first frame of the original observed centroid position time series are taken and assigned to the horizontal and vertical coordinate components of the augmented state vector, respectively. The initial velocity is calculated by dividing the difference between the horizontal coordinates of the second and first frames of the original observed centroid position time series by the frame interval to obtain the horizontal initial velocity, and by dividing the difference between the vertical coordinates of the second and first frames by the frame interval to obtain the vertical initial velocity. The frame interval is the reciprocal of the image acquisition frame rate. The horizontal and vertical initial velocities are then assigned to the horizontal and vertical velocity components of the augmented state vector, respectively. Finally, the horizontal and vertical deviation components of the first frame of the centroid offset error prediction sequence are taken and assigned to the horizontal and vertical deviation components of the augmented state vector, respectively. The estimation error covariance matrix is ​​initialized as a 6x6 diagonal matrix, with each element on the diagonal being the square of the estimated uncertainty of the corresponding state component. Specifically, the diagonal elements corresponding to the horizontal and vertical coordinates are 100, the diagonal elements corresponding to the horizontal and vertical velocities are 400, the diagonal elements corresponding to the horizontal and vertical deviation components are 25, and the off-diagonal elements are all 0.

[0040] Starting from the second frame, the posterior estimate of the augmented state vector updated in the previous frame is substituted into the state transition relation of the augmented state space model. The transition of the state component of the true centroid position is calculated based on the recursive relation of the particle flight dynamics, and the transition of the state component of the spin error is calculated by adding the difference between adjacent frames of the centroid offset error prediction sequence as an increment. After calculation, the prior estimate of the augmented state vector of the current frame is obtained. At the same time, covariance propagation is performed on the estimation error covariance matrix of the previous frame. The partial derivatives of the state transition relation with respect to each component of the six-dimensional augmented state vector are used to construct a 6-row, 6-column state transition Jacobian matrix. This Jacobian matrix is ​​then multiplied left by the estimation error covariance matrix of the previous frame and right by the transpose of the Jacobian matrix. The process noise covariance matrix is ​​added. The process noise covariance matrix is ​​a diagonal matrix. The noise variance corresponding to the horizontal and vertical coordinates in the diagonal elements is set to 1, the noise variance corresponding to the horizontal and vertical velocities is set to 4, and the noise variance corresponding to the horizontal and vertical deviation components is set to 0.01. This yields the prior estimation error covariance matrix of the current frame.

[0041] The horizontal coordinate component and the horizontal deviation component are extracted from the prior estimate of the augmented state vector in the current frame and added together to obtain the predicted observed horizontal coordinate. The vertical coordinate component and the vertical deviation component are extracted and added together to obtain the predicted observed vertical coordinate. The horizontal and vertical coordinates in the time series of the original observed centroid position of the current frame are taken as the actual observations. The predicted observed horizontal coordinate is subtracted from the actual observed horizontal coordinate to obtain the horizontal measurement residual, and the predicted observed vertical coordinate is subtracted from the actual observed vertical coordinate to obtain the vertical measurement residual. The two residuals form a 2D measurement residual vector. The observation Jacobian matrix is ​​obtained by taking the partial derivatives of the observation relationship with each component of the six-dimensional augmented state vector. It is a 2x6 matrix, where the partial derivatives of the horizontal observation with respect to the horizontal coordinate and the horizontal deviation component are both 1, the partial derivatives of the vertical observation with respect to the vertical coordinate and the vertical deviation component are both 1, and the remaining partial derivatives are 0. Multiply the prior estimation error covariance matrix on the left by the transpose of the observation Jacobian matrix, then multiply the observation Jacobian matrix on the left by the prior estimation error covariance matrix on the right by the transpose of the observation Jacobian matrix, add the observation noise covariance matrix, invert the result, and multiply by the result to obtain a 6-row, 2-column gain matrix.

[0042] The observation noise covariance matrix is ​​a 2x2 diagonal matrix with diagonal elements of value 25. Multiplying the gain matrix by the 2D measurement residual vector yields a 6-dimensional positive vector. Adding the augmented state vector prior estimate to the corresponding components of the correction vector gives the posterior estimate of the augmented state vector for the current frame. Simultaneously, the estimation error covariance matrix is ​​updated by subtracting the gain matrix multiplied by the observation Jacobian matrix from the 6-dimensional identity matrix and left-multiplying the result by the prior estimation error covariance matrix to obtain the posterior estimation error covariance matrix for the current frame, which is used in the next frame. The first component (horizontal coordinates) and the second component (vertical coordinates) are extracted from the posterior estimate of the augmented state vector for the current frame and used as the corrected centroid coordinates for the current frame. Starting from the second frame, the above prediction and update steps are performed frame by frame, outputting a pair of corrected centroid coordinates for each frame. The corrected centroid coordinates of all frames are then sorted in ascending order by frame number to generate and output the actual flight trajectory data.

[0043] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. The semiconductor medium can be a solid-state drive.

[0044] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0045] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and modules described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0046] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or modules may be electrical, mechanical, or other forms.

[0047] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical modules; they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0048] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0049] 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 application, in essence, or the part that contributes to the prior art, or a portion 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 application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0050] The above description is merely a specific embodiment of this application, but the scope of protection of this application 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 this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0051] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for correcting badminton trajectory data based on flight dynamics constraints, characterized in that, Includes the following steps: S1. Collect image sequences of badminton shuttlecock flight, extract the badminton shuttlecock region in the image frame by frame, and calculate the pixel coordinates using the gray-scale centroid method to generate the original observation centroid position time series. S2. Based on the aerodynamic drag coefficient and lift coefficient of badminton flight, establish the recursive relationship of particle flight dynamics. Using the original observed centroid position time series as input, perform forward prediction and backward smoothing to generate a smooth reference trajectory. Then, calculate the difference between the original observed centroid position time series and the smooth reference trajectory frame by frame to obtain the observation residual time series. S3. Apply a sliding time window to the observed residual time series and calculate the power spectral density. Extract the periodic components whose energy proportion exceeds the preset threshold and whose frequency decreases monotonically with time. Identify the instantaneous frequency curve and amplitude envelope curve of the periodic components. S4. Establish a mapping function between the badminton shuttlecock spin rate and the centroid offset vector, convert the instantaneous frequency curve into a spin rate decay curve, and use the spin rate decay curve and amplitude envelope curve as inputs to generate a centroid offset error prediction sequence that changes synchronously with the flight phase. The mapping function between the badminton shuttle's spin rate and the centroid offset vector is obtained by acquiring badminton shuttle images at different spin rates, calculating the gray-scale centroid coordinates and the true geometric center coordinates for each frame of the image, and using the coordinate difference between the two as the centroid offset vector corresponding to the spin rate. The relationship between the horizontal and vertical components of the centroid offset vector and the spin rate is fitted with a cubic polynomial, and the two polynomial functions obtained together constitute the mapping function between the spin rate and the centroid offset vector. S5. Update the true center of mass position state variables according to the recursive relationship of flight dynamics, update the spin error state variables according to the predicted sequence of center of mass offset error, and form the predicted observation values ​​by combining the true center of mass position state variables and the spin error state variables to construct an augmented state space model. S6. Input the original observed centroid position time series into the augmented state space model. Based on the measurement residual between the predicted observation and the original observed centroid position, recursively correct the augmented state vector to obtain the corrected centroid coordinates and generate flight trajectory data.

2. The badminton trajectory data correction method based on flight dynamics constraints according to claim 1, characterized in that, Specifically, S1 includes: For each frame of image, the gradient magnitude is calculated at multiple scales, and connected components with closed contours are extracted as candidate badminton shuttlecock regions. The badminton shuttlecock region of the current frame is determined based on the matching degree between the area and contour curvature features of the candidate badminton shuttlecock regions and the confirmed badminton shuttlecock regions of the previous frame. Subtract the average gray value of pixels in the annular neighborhood that extends outward from the bounding rectangle of the determined badminton area from the gray value of the pixels in the determined badminton area as the background compensation term. Perform square weighting on the compensated gray value and calculate the weighted gray centroid coordinates as the pixel coordinates of the current frame. Repeat the above process frame by frame, and arrange the pixel coordinates obtained from each frame in chronological order to generate the original observation centroid position time series.

3. The badminton trajectory data correction method based on flight dynamics constraints according to claim 1, characterized in that, Specifically, S2 includes: The aerodynamic drag coefficient and lift coefficient of badminton shuttlecock flight are obtained, and a recursive relationship of the dynamics of point mass flight is constructed based on the aerodynamic drag coefficient and lift coefficient. The recursive relationship uses the current position, velocity and acceleration of the center of mass as state variables, and air density, shuttlecock mass and reference area as recursive constants. Using the first frame of the original observed centroid position time series as the initial state, the recursive relation is used to calculate the predicted centroid position frame by frame along the increasing time direction to generate the forward predicted trajectory; using the last frame of the original observed centroid position time series as the final state, the recursive relation is used to calculate the estimated centroid position frame by frame along the decreasing time direction to generate the backward smoothed trajectory. The forward predicted trajectory position and the backward smoothed trajectory position corresponding to the same frame are fused, and the fusion result is used as the smoothed reference trajectory position; the centroid position of each frame in the original observed centroid position time series is subtracted from the smoothed reference trajectory position, and the resulting difference sequence is used as the observed residual time series.

4. The badminton trajectory data correction method based on flight dynamics constraints according to claim 1, characterized in that, Specifically, S3 includes: Set the window length and step size parameters of the sliding time window. The window length parameter is greater than the estimated period of the badminton shuttlecock spin motion. The observed residual time series is segmented from the starting frame according to the step size parameter to obtain a set of time window residual segments. For each time window residual segment, the power spectral density is calculated, and the frequency corresponding to the maximum peak of the power spectral density is found as the dominant frequency of the current time window. The ratio of the peak energy corresponding to the dominant frequency to the total energy of the entire frequency band is calculated as the energy proportion of the current time window. Candidate frequency segments with energy proportions exceeding a preset threshold and dominant frequencies decreasing in time order are selected from the dominant frequency sequences corresponding to adjacent time windows. The center frequency of the time window corresponding to each candidate frequency segment is linearly interpolated to generate a periodic component frequency decay trajectory consistent with the length of the observed residual time series. Using the frequency decay trajectory of the periodic component as the center frequency, bandpass filtering is performed frame by frame on the observed residual time series. The instantaneous frequency curve of the periodic component is calculated based on the time interval between adjacent zero crossings in the filtered time series signal. At the same time, Hilbert transform is performed on the filtered time series signal, and the magnitude of the complex envelope is used as the amplitude envelope curve of the periodic component.

5. The method for correcting badminton trajectory data based on flight dynamics constraints according to claim 1, characterized in that, Specifically, S4 includes: The frequency value of each frame in the instantaneous frequency curve is converted into the spin rate of the corresponding frame according to the preset proportional coefficient between frequency and spin rate, and the spin rate decay curve is calculated frame by frame. The amplitude envelope curve is normalized to obtain the amplitude modulation coefficients corresponding to each frame. The spin rate value of each frame in the spin rate decay curve is substituted into the mapping function to obtain the reference centroid offset vector corresponding to that frame. The reference centroid offset vector is scaled by the amplitude modulation coefficient of the same frame to obtain the centroid offset error prediction vector of that frame. After frame-by-frame calculation, a centroid offset error prediction sequence that changes synchronously with the flight phase is generated.

6. The method for correcting badminton trajectory data based on flight dynamics constraints according to claim 1, characterized in that, Specifically, S5 includes: The true centroid position state variables are the horizontal coordinates, vertical coordinates, horizontal velocity, and vertical velocity of the badminton shuttlecock in the image pixel coordinate system, and the spin error state variables are the horizontal and vertical deviation components of the centroid offset error prediction sequence in the current frame. The true center of mass position state variable and the spin error state variable are concatenated end to end to form a six-dimensional augmented state vector; the true center of mass position state variable is updated frame by frame according to the recursive relationship of the particle flight dynamics, and the spin error state variable is updated frame by frame according to the difference between the predicted values ​​of two adjacent frames in the center of mass offset error prediction sequence. The augmented state space model is constructed by adding the horizontal coordinate of the true centroid position state variable to the horizontal deviation component of the spin error state variable, and adding the vertical coordinate to the vertical deviation component to form the predicted observation value.

7. The method for correcting badminton trajectory data based on flight dynamics constraints according to claim 1, characterized in that, Specifically, S6 includes: The augmented state vector is initialized with the original centroid position coordinates of the first frame, the initial velocity calculated based on the continuous observation frames, and the predicted centroid offset error value of the first frame. The estimated error covariance matrix is ​​initialized as a diagonal matrix. Starting from the second frame, the posterior estimate of the augmented state vector of the previous frame is substituted into the augmented state space model to obtain the prior estimate of the augmented state vector of the current frame, and the estimated error covariance matrix is ​​updated. Based on the measurement residual between the original observed centroid position and the predicted observed value in the current frame, the gain matrix is ​​calculated using the estimated error covariance matrix and the observation Jacobian matrix. The prior estimate of the augmented state vector is then corrected to obtain the posterior estimate of the augmented state vector in the current frame. The observed Jacobian matrix is ​​a 2-row, 6-column matrix, generated by taking the partial derivatives of the horizontal and vertical coordinates of the predicted observed values ​​with respect to each state component of the six-dimensional augmented state vector. Extract the horizontal and vertical coordinates of the true centroid position state variable from the posterior estimate of the augmented state vector of the current frame as the corrected centroid coordinates. After executing frame by frame, arrange the flight trajectory data in frame order and output it.

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