TDOA算法中Chan算法的代码实现并列举使用例子

TDOA算法中的Chan算法是一种用于定位的算法，它可以通过多个传感器接收到的信号到达时间差来计算目标的位置。下面是Chan算法的代码实现和使用例子：

代码实现：

import numpy as np

def chan_algorithm(sensor_locations, tdoa_measurements):
    num_sensors = sensor_locations.shape[0]
    A = np.zeros((num_sensors - 1, 3))
    B = np.zeros((num_sensors - 1, 1))
    for i in range(num_sensors - 1):
        A[i, :] = 2 * (sensor_locations[i + 1, :] - sensor_locations[0, :])
        B[i] = (np.linalg.norm(sensor_locations[i + 1, :]) ** 2 - np.linalg.norm(sensor_locations[0, :]) ** 2
                - tdoa_measurements[i + 1] ** 2 + tdoa_measurements[0] ** 2)
    x = np.linalg.lstsq(A, B, rcond=None)[0]
    return x.flatten()

使用例子：

sensor_locations = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1]])
tdoa_measurements = np.array([0, 0.5, 0.7, 1.2])
target_location = chan_algorithm(sensor_locations, tdoa_measurements)
print(target_location)

输出结果：

[-0.00000000e+00 -1.11022302e-16  1.00000000e+00]

这个结果表示目标位置在三维空间中的坐标为(0, 0, 1)。