Trajectory Angles Evaluation for the Flight Vehicle via Wavelet Transforms and Similarity Measures
Kunkun Li, Mingrui Qi, Rui Cao · 2023
In the flight vehicle test, the evaluation of trajectory parameters, such as trajectory inclination angles and trajectory deflection angles, is sometimes required. To do that, we propose an evaluation method based on the wavelet transform and similarity measure. Concretely, since the wavelet transform possesses both smoothing and derivation operations in certain cases, Gaussian and Gaussian-1 wavelet functions are respectively used for wavelet transforms on the non-stationary position components series of the flight vehicle’s trajectory that is reconstructed using noisy radar measurements. As a result, the smoothed position components series and their first derivative series are respectively obtained, wherein the latter can be viewed as the flight velocity components series, and further utilized to calculate the two types of real trajectory angle series. Then, by multi-point matching and comparisons, the average time bias between the flight vehicle’s trajectory series in reality and that in theory is approximately estimated, such that the two types of trajectory angle series in reality and those in theory can be respectively aligned over time via the Lagrange polynomial interpolation. Finally, the correlation coefficients are employed to measure and evaluate the similarities of these time-aligned trajectory angle series. A simulation experiment is provided and carried out to demonstrate the feasibility of the proposed method.