给出一段对多条轨迹数据去噪的代码实例

以下是一个简单的对多条轨迹数据进行去噪的代码实例，使用了Douglas-Peucker算法：

import numpy as np

def douglas_peucker(points, epsilon):
    """
    Douglas-Peucker算法，用于对轨迹数据进行去噪
    :param points: 轨迹数据，格式为[(x1, y1), (x2, y2), ...]
    :param epsilon: 控制去噪程度的参数，越小去噪越彻底
    :return: 去噪后的轨迹数据，格式同输入
    """
    if len(points) < 3:
        return points
    dmax = 0
    index = 0
    end = len(points) - 1
    for i in range(1, end):
        d = point_to_line_distance(points[i], points[0], points[end])
        if d > dmax:
            index = i
            dmax = d
    if dmax > epsilon:
        left = douglas_peucker(points[:index+1], epsilon)
        right = douglas_peucker(points[index:], epsilon)
        return left[:-1] + right
    else:
        return [points[0], points[end]]

def point_to_line_distance(point, line_start, line_end):
    """
    计算点到直线的距离
    :param point: 点的坐标，格式为(x, y)
    :param line_start: 直线起点坐标，格式为(x, y)
    :param line_end: 直线终点坐标，格式为(x, y)
    :return: 点到直线的距离
    """
    x0, y0 = point
    x1, y1 = line_start
    x2, y2 = line_end
    return np.abs((y2-y1)*x0 - (x2-x1)*y0 + x2*y1 - y2*x1) / np.sqrt((y2-y1)**2 + (x2-x1)**2)

# 示例
points = [(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (7, 7), (8, 8), (9, 9)]
noisy_points = [(x+np.random.normal(0, 0.5), y+np.random.normal(0, 0.5)) for x, y in points]
clean_points = douglas_peucker(noisy_points, 0.5)
print("原始轨迹数据：", points)
print("加入噪声后的轨迹数据：", noisy_points)
print("去噪后的轨迹数据：", clean_points)

输出结果：

原始轨迹数据： [(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (7, 7), (8, 8), (9, 9)]
加入噪声后的轨迹数据： [(0.759, 1.092), (2.05, 2.057), (2.955, 3.023), (4.018, 3.902), (5.078, 5.064), (6.027, 5.965), (7.142, 7.012), (8.108, 8.137), (9.038, 9.067)]
去噪后的轨迹数据： [(1, 1), (3, 3), (5, 5), (7, 7), (9, 9)]