蒙特卡洛粒子滤波定位算法源代码
时间: 2023-07-10 09:33:28 浏览: 52
以下是一个简单的Python实现蒙特卡洛粒子滤波定位算法的源代码,供您参考:
```python
import numpy as np
# 运动模型
def motion_model(x, u):
# 假设机器人在x位置,执行u运动后到达x_prime位置
x_prime = np.array([x[0] + u[0]*np.cos(x[2]),
x[1] + u[0]*np.sin(x[2]),
x[2] + u[1]])
return x_prime
# 传感器模型
def sensor_model(x, z, sensor_std):
# 计算机器人在x位置,测量z的概率
z_true = np.array([np.sqrt((landmark[0] - x[0])**2 + (landmark[1] - x[1])**2) for landmark in landmarks])
prob = np.exp(-0.5*(z - z_true)**2/sensor_std**2)
return np.prod(prob)
# 初始化粒子权重
def initialize_particles(num_particles):
particles = np.zeros((num_particles, 3)) # 每个粒子包含(x, y, theta)三个状态
particles[:, :2] = np.random.uniform(low=[0, 0], high=[10, 10], size=(num_particles, 2)) # x, y坐标随机初始化
particles[:, 2] = np.random.uniform(low=-np.pi, high=np.pi, size=num_particles) # theta方向随机初始化
weights = np.ones(num_particles)/num_particles # 初始权重均为1/N
return particles, weights
# 粒子更新
def update_particles(particles, u, sensor_std):
for i in range(particles.shape[0]):
# 运动模型更新
particles[i] = motion_model(particles[i], u)
# 传感器模型更新
weights[i] *= sensor_model(particles[i], z, sensor_std)
weights /= np.sum(weights) # 归一化权重
return particles, weights
# 粒子重采样
def resample_particles(particles, weights):
indices = np.random.choice(particles.shape[0], size=particles.shape[0], replace=True, p=weights)
return particles[indices], np.ones(particles.shape[0])/particles.shape[0]
# 主函数
if __name__ == '__main__':
num_particles = 1000 # 粒子数
landmarks = np.array([[2, 2], [8, 8]]) # 地标坐标
sensor_std = 0.1 # 传感器噪声方差
x_true = np.array([2, 2, np.pi/4]) # 真实初始位置
z = np.array([np.sqrt((landmark[0] - x_true[0])**2 + (landmark[1] - x_true[1])**2) for landmark in landmarks]) # 测量结果
particles, weights = initialize_particles(num_particles) # 初始化粒子
for t in range(100):
u = np.array([1, np.pi/10]) # 机器人运动控制量
particles, weights = update_particles(particles, u, sensor_std) # 粒子更新
if np.sum(weights**2)/np.sum(weights) < num_particles/2: # 如果权重方差过小,进行重采样
particles, weights = resample_particles(particles, weights)
x_est = np.average(particles, weights=weights, axis=0)
print(f"t={t}, x_true={x_true}, x_est={x_est}")
```
上述代码实现了一个简单的二维机器人在已知两个地标的环境中进行定位的过程。您可以根据实际应用场景进行相应的修改和优化。