给出一个轨迹数据集去噪的代码实例

以下是一个基于Python的轨迹数据集去噪的代码实例：

import numpy as np
from scipy.spatial.distance import cdist

def douglas_peucker(points, epsilon):
    """
    Douglas-Peucker algorithm for line simplification.
    """
    dmax = 0
    index = 0
    end = len(points) - 1
    for i in range(1, end):
        d = perpendicular_distance(points[i], points[0], points[end])
        if d > dmax:
            index = i
            dmax = d
    if dmax > epsilon:
        results1 = douglas_peucker(points[:index+1], epsilon)
        results2 = douglas_peucker(points[index:], epsilon)
        results = np.vstack((results1[:-1], results2))
    else:
        results = np.vstack((points[0], points[end]))
    return results

def perpendicular_distance(point, start, end):
    """
    Calculate the perpendicular distance between a point and a line.
    """
    if np.array_equal(start, end):
        return np.linalg.norm(point - start)
    else:
        return np.divide(np.abs(np.linalg.norm(np.cross(end - start, start - point))), np.linalg.norm(end - start))

def remove_duplicates(points):
    """
    Remove duplicate points from a list of points.
    """
    return np.unique(points, axis=0)

def remove_close_points(points, min_distance):
    """
    Remove points that are too close to each other.
    """
    distances = cdist(points, points)
    np.fill_diagonal(distances, np.inf)
    mask = np.all(distances > min_distance, axis=1)
    return points[mask]

def smooth(points, window_size):
    """
    Smooth a list of points using a moving average filter.
    """
    kernel = np.ones(window_size) / window_size
    return np.convolve(points, kernel, mode='same')

def denoise(points, epsilon=1.0, min_distance=0.1, window_size=5):
    """
    Denoise a list of points using the Douglas-Peucker algorithm,
    removing duplicates and close points, and smoothing the result.
    """
    points = douglas_peucker(points, epsilon)
    points = remove_duplicates(points)
    points = remove_close_points(points, min_distance)
    points = smooth(points, window_size)
    return points

这个代码实例使用了Douglas-Peucker算法对轨迹数据进行了去噪处理，同时还去除了重复点和过于接近的点，并使用了移动平均滤波对结果进行了平滑处理。