Vehicle trajectory prediction based on EKF-GRU

doi:10.16265/j.cnki.issn1003-3033.2024.06.0720

Abstract

Abstract:

To enhance the driving safety and achieve correct decision planning for autonomous vehicles, a safe driving trajectory prediction method based on EKF-GRU was proposed. By combining learning-based methods with physics-based approaches, the prediction accuracy was improved and the rationality of the predicted trajectories was enhanced. In the first step of this method, a prediction network was constructed based on GRU to predict the longitudinal acceleration and yaw angular velocity of vehicles by extracting historical trajectory features. In the second step, an EKF state estimator was built based on the nonlinear vehicle kinematics to generate the vehicle's future limited-time trajectory, incorporating the observations obtained previously. The trajectory prediction method was validated on the NGSIM I-80 and US-101 multi-vehicle trajectory datasets. Experimental results demonstrate that the final distance errors (FDE), root mean square errors (RMSE), and average distance errors (ADE) of the predicted trajectories generated by traditional physics-based methods are 6.48, 7.69 and 3.03 meters, respectively. In contrast, trajectories predicted using EKF-GRU exhibit higher accuracy, and the corresponding values are 5.45, 6.67 and 2.56 meters, respectively. This represents improvements of 15.90%, 13.26% and 15.51%.

Key words: extended Kalman filtering (EKF), gate recurrent unit (GRU), vehicle trajectory, trajectory prediction, next generation simulation (NGSIM) dataset, neural network

CLC Number:

X951交通运输安全

ZHANG Chuanying, XU Guoyan, CHEN Zhifa, ZHOU Bin, CHEN Liwei, HONG Wei. Vehicle trajectory prediction based on EKF-GRU[J]. China Safety Science Journal, 2024, 34(6): 164-172.

Figures/Tables 13

Fig.1

Fig.2

Fig.3

Table 1

Encoder-Decoder network architecture

网络架构:
层级:	4×1
输入层:	1-D, $X \in R^{128 \times 30}$ $X ∈ R 128 × 30$
GRU层:	80Units $h_{k} \in R^{128 \times 256}$ $h k ∈ R 128 × 256$
$\begin{array}{l} W_{x r}, W_{x z}, W_{x h} \in R^{30 \times 256}, W_{h r}, W_{h z}, W_{h h} \in R^{256 \times 256}, \\ b_{r}, b_{z}, b_{h} \in R^{1 \times 256} \end{array}$ $W x r, W x z, W x h ∈ R 30 × 256, W h r, W h z, W h h ∈ R 256 × 256, b r, b z, b h ∈ R 1 × 256$
全连接层:	$W_{F C} \in R^{50 \times 50}$ $W F C ∈ R 50 × 50$
输出层:	Regression

Table 1

Fig.4

算法1 EKF- GRU轨迹预测

需求:

Q, R

$Q, R$
for k from 0 to 49 step 1 do

Z {(a, ω)}_{k + 1}^{i}, R (σ_{a}^{2}, σ_{ω}^{2})_{k + 1}^{i} \leftarrow G R U ({\hat{X}}_{k = (k - 29) ~ k}^{i})

$Z (a, ω) k + 1 i, R (σ a 2, σ ω 2) k + 1 i ← G R U (X^k = (k - 29) ~ k i)$

{\hat{X}}_{k + 1}^{i}, {\hat{P}}_{k + 1}^{i} \leftarrow E K F (Z {(a, ω)}_{k + 1}^{i}, {\hat{X}}_{k}^{i}, {\hat{P}}_{k}^{i}, Q, R (σ_{a}^{2}, σ_{ω}^{2})_{k + 1}^{i})

$X^k + 1 i, P^k + 1 i ← E K F (Z (a, ω) k + 1 i, X^k i, P^k i, Q, R (σ a 2, σ ω 2) k + 1 i)$
end for
return

({\hat{X}}_{k + 1}^{i}, {\hat{P}}_{k + 1}^{i})_{k = 0 ~ 49}^{i = 1 ~ N}

$(X^k + 1 i, P^k + 1 i) k = 0 ~ 49 i = 1 ~ N$

Fig.5

Fig.6

算法2 数据平滑过滤过程
需求: $Q, R$ $Q, R$
设置: ${\hat{X}}_{- 30}, {\hat{P}}_{- 30}$ $X^- 30, P^- 30$
for k from-30 to -1 step 1 do ${\hat{X}}_{k + 1}, {\hat{P}}_{k + 1} \leftarrow K F (Z_{k + 1}, {\hat{X}}_{k}, {\hat{P}}_{k}, Q, R)$ $X^k + 1, P^k + 1 ← K F (Z k + 1, X^k, P^k, Q, R)$ end for
$X = M A (\hat{X})$ $X = M A (X^)$

Fig.7

Fig.8

Table 2

Fig.9

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预测步长/s		1	2	3	4	5
FDE	EKF-CTRV	0.61	1.76	2.98	4.65	6.48
FDE	EKF-GRU^*	0.61	1.51	2.52	4.09	5.45
RMSE	EKF-CTRV	0.81	2.03	3.62	5.84	7.69
RMSE	EKF-GRU^*	0.76	1.78	3.18	4.73	6.67
ADE	EKF-CTRV	3.03
ADE	EKF-GRU^*	2.56

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