### HIVT 轨迹预测算法实现
对于HIVT（History-based Interactive Vehicle Trajectory）轨迹预测，一种常见的做法是利用历史位置数据对未来路径进行建模。考虑到预测的未来轨迹被归一化为每个智能体最近观察到的位置[^1]，下面是一个简化版的Python代码示例，展示如何基于过去观测构建简单的线性回归模型来进行车辆运动预测。
```python
import numpy as np
from sklearn.linear_model import LinearRegression
def normalize_trajectories(trajectories, recent_positions):
"""Normalize trajectories based on the most recently observed positions."""
normalized = []
for i, traj in enumerate(trajectories):
offset = recent_positions[i]
norm_traj = [(point[0]-offset[0], point[1]-offset[1]) for point in traj]
normalized.append(norm_traj)
return np.array(normalized)
def predict_future_trajectory(historical_data, steps_ahead=5):
"""
Predict future trajectory using historical data.
Parameters:
- historical_data: List of tuples representing (time_step, x_position, y_position).
- steps_ahead: Number of time steps into the future to predict.
Returns:
A list containing predicted coordinates at each step ahead.
"""
times, xs, ys = zip(*historical_data[-steps_ahead:])
X_train = np.array(times).reshape(-1, 1)
model_x = LinearRegression().fit(X_train, xs)
model_y = LinearRegression().fit(X_train, ys)
future_times = range(max(times)+1, max(times)+steps_ahead+1)
predictions = [
(
int(model_x.predict([[t]])[0]),
int(model_y.predict([[t]])[0])
)
for t in future_times
]
return predictions
# Example usage
if __name__ == "__main__":
# Sample input: Time series of vehicle locations over several seconds
sample_historical_data = [
(0, 10, 20), (1, 12, 22), (2, 14, 24),
(3, 17, 26), (4, 20, 28), (5, 23, 30)
]
prediction_steps = 3
pred = predict_future_trajectory(sample_historical_data, prediction_steps)
print(f"Predicted next {prediction_steps} steps:", pred)
```
此代码片段展示了如何使用线性回归来预测给定时间序列内的下一组坐标点。实际应用中可能还需要考虑更多因素，比如速度变化率、加速度以及其他环境变量的影响。
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