Abstract:
The article presents a method for smoothing the trajectory obtained using high-frequency data on the movement of motor vehicles over rough terrain in order to improve the accuracy and smoothness of trajectories in the presence of noise. The main attention is paid to the features of the application of quintic B-splines, which provide a high degree of smoothness in describing the trajectory and preliminary data filtering. The article consistently describes the technical and mathematical difficulties that arise when implementing the algorithm on real data, and suggests methods for overcoming them. One of such methods is filtering outliers to eliminate sharp deviations from the original trajectory using a digital Butterworth filter. Various approaches for working with a large number of trajectory points are considered and tested, including splitting the data into separate overlapping windows with their sequential stitching, which significantly improves the performance of the algorithm. To optimize the calculations, it is also proposed to use sparse matrices that effectively work with large amounts of data and occupy significantly less computer memory compared to traditional ones. The effectiveness of the proposed approach is confirmed by examples where smoothed trajectories obtained from noisy data are visualized.
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