CoPAD: Cooperative V2X Trajectory Prediction

• CoPAD is a cooperative trajectory prediction framework that early-fuses multi-source raw trajectories using the Hungarian algorithm and Kalman filtering to mitigate occlusion and other sensing limitations.
• It integrates a graph-based spatio-temporal encoder with Past Time Attention and mode attention to model interactions and predict diverse future trajectories via sparse anchor decoding.
• Empirical results on DAIR-V2X-Seq show CoPAD achieves competitive minFDE and miss rate with a reduced parameter count, affirming the benefits of early fusion in cooperative settings.

Searching arXiv for CoPAD and closely related V2X trajectory prediction papers to ground the article. CoPAD is a cooperative trajectory prediction framework for Vehicle-to-Everything (V2X) scenarios that combines multi-source raw trajectory fusion with a graph-based spatio-temporal encoder, a mode attention mechanism, and an anchor-oriented decoder (Wu et al., 19 Sep 2025). It is designed for settings in which single-vehicle perception is degraded by occlusion, long distances, or adverse weather, and addresses those limitations by performing early fusion of vehicle and road infrastructure trajectories. In the formulation reported for CoPAD, vehicle-side history and infrastructure-side history are matched with the Hungarian algorithm, fused with Kalman filtering, encoded through Past Time Attention (PTA), diversified through a mode attention module, and decoded into complete future trajectories using sparse oriented anchors (Wu et al., 19 Sep 2025).

1. Problem formulation and V2X motivation

CoPAD is situated in the trajectory prediction literature for autonomous driving, specifically in the cooperative setting where both vehicles and road-side units (RSUs) contribute observations (Wu et al., 19 Sep 2025). In the single-vehicle setting, raw trajectories of surrounding agents are obtained only from the ego vehicle’s onboard sensors, including LiDAR and camera. The reported motivation is that real traffic conditions introduce missing or highly noisy trajectories through occlusions, long distances, and adverse weather, which in turn degrades prediction accuracy (Wu et al., 19 Sep 2025).

The framework leverages Vehicle-to-Everything communication so that infrastructure viewpoints can supplement vehicle viewpoints. The central design premise is “early fusion” of raw trajectories rather than a purely feature-level fusion strategy. In the reported interpretation, this improves trajectory completeness by filling in missing observations and reduces sparsity before downstream encoding and prediction (Wu et al., 19 Sep 2025). This suggests that CoPAD treats cooperative perception not merely as an auxiliary cue, but as a direct means of repairing the input trajectory history presented to the predictor.

The model is described as lightweight and end-to-end. Its main components are explicitly enumerated as: a fusion module based on the Hungarian algorithm and Kalman filtering, a PTA encoder for spatio-temporal and map interactions, a mode attention module for multi-modal diversity, and an anchor-oriented decoder (AoD) for final trajectory generation (Wu et al., 19 Sep 2025).

2. Multi-source trajectory fusion

CoPAD defines the vehicle-side observed history as

$$\mathcal T_V = \bigl[p^{(1)},\dots,p^{(t_h)}\bigr]\in\mathbb R^{N_t\times t_h\times C_t},$$

and the infrastructure-side history as

$$\mathcal T_I\in\mathbb R^{M_t\times t_h\times C_t}.$$

The fusion is performed directly on these raw trajectories in three stages (Wu et al., 19 Sep 2025).

First, objects across the two sources are matched at the first and last time steps by solving a linear assignment problem with the Hungarian algorithm. Given a pairwise distance cost matrix $C\in\mathbb R^{N_t\times M_t}$, the assignment matrix $X\in\{0,1\}^{N_t\times M_t}$ is obtained by minimizing

$$\min_{X}\;\sum_{i=1}^{N_t}\sum_{j=1}^{M_t} C_{ij}\,X_{ij}, \quad X\mathbf1 = \mathbf1,\; X^T\mathbf1 \le \mathbf1\,.$$

This step determines which vehicle-side and infrastructure-side trajectories correspond to the same physical object (Wu et al., 19 Sep 2025).

Second, the matched and unmatched sets are separated as

$$\mathcal T_{\rm matched} \;=\;\mathcal H(\mathcal T_V,\mathcal T_I), \quad \mathcal T_{\rm unmatched} \;=\;\bigl(\mathcal T_V\cup\mathcal T_I\bigr)\setminus\mathcal T_{\rm matched}.$$

Third, each matched pair is fused through a Kalman filtering operator $\mathcal K$, and the unmatched trajectories are concatenated: $$\mathcal T_{\rm fusion} \;=\; \mathcal K\bigl(\mathcal T_{\rm matched}\bigr)\;\cup\;\mathcal T_{\rm unmatched}\,.$$ Although CoPAD treats $\mathcal K$ as a black-box fusion operator, the standard Kalman filter update equations are given: $$\hat x_{t|t-1} = A\,\hat x_{t-1|t-1},\quad S_t = H\,P_{t|t-1}H^\top + R,\quad K_t = P_{t|t-1}H^\top S_t^{-1},\quad \hat x_{t|t} = \hat x_{t|t-1} + K_t\bigl(z_t - H\,\hat x_{t|t-1}\bigr).$$ Within the reported system design, the purpose of this module is to construct trajectories with higher completeness and accuracy prior to graph encoding (Wu et al., 19 Sep 2025).

Ablation results attribute a clear advantage to this raw-data fusion strategy over feature-level alternatives. In the reported comparison, early fusion with Kalman filter outperforms intermediate fusion by addition (“IA”) and intermediate fusion by concatenation (“IC”) (Wu et al., 19 Sep 2025). This supports the specific architectural decision to repair and merge observation sequences before feature extraction rather than after.

3. PTA encoder and heterogeneous graph construction

After fusion, CoPAD builds a heterogeneous spatio-temporal graph at each time step $$\mathcal T_I\in\mathbb R^{M_t\times t_h\times C_t}.$$0, with nodes for observed agents and lane segments from the vectorized HD map (Wu et al., 19 Sep 2025). A graph attention network (GAT) is first applied to extract per-node features

$$\mathcal T_I\in\mathbb R^{M_t\times t_h\times C_t}.$$1

This graph stage incorporates both agent interactions and map context.

To model interactions across historical frames, CoPAD introduces Past Time Attention (PTA). Given a look-back window $$\mathcal T_I\in\mathbb R^{M_t\times t_h\times C_t}.$$2, for each $$\mathcal T_I\in\mathbb R^{M_t\times t_h\times C_t}.$$3 the historical context is formed as

$$\mathcal T_I\in\mathbb R^{M_t\times t_h\times C_t}.$$4

and the current features are repeated as

$$\mathcal T_I\in\mathbb R^{M_t\times t_h\times C_t}.$$5

The encoder output is then defined by

$$\mathcal T_I\in\mathbb R^{M_t\times t_h\times C_t}.$$6

Here, MHCA denotes multi-head cross-attention (Wu et al., 19 Sep 2025).

The paper specifies the standard attention projections

$$\mathcal T_I\in\mathbb R^{M_t\times t_h\times C_t}.$$7

and for each attention head,

$$\mathcal T_I\in\mathbb R^{M_t\times t_h\times C_t}.$$8

The stated function of PTA is to capture global interactions across past frames, complementing the per-frame GAT representation (Wu et al., 19 Sep 2025).

The ablation study identifies PTA as the most consequential individual module. Under Kalman-filter fusion with mode attention and two anchors, removing PTA changes the reported metrics from minADE $$\mathcal T_I\in\mathbb R^{M_t\times t_h\times C_t}.$$9, minFDE $C\in\mathbb R^{N_t\times M_t}$0, MR $C\in\mathbb R^{N_t\times M_t}$1 to minADE $C\in\mathbb R^{N_t\times M_t}$2, minFDE $C\in\mathbb R^{N_t\times M_t}$3, MR $C\in\mathbb R^{N_t\times M_t}$4 (Wu et al., 19 Sep 2025). The paper summarizes this as the largest single improvement, with minADE reduced from $C\in\mathbb R^{N_t\times M_t}$5 to $C\in\mathbb R^{N_t\times M_t}$6 when PTA is introduced in the corresponding comparison. This suggests that explicit temporal cross-frame interaction modeling is central to CoPAD’s reported performance profile.

4. Mode attention and multi-modal prediction

CoPAD models future uncertainty through $C\in\mathbb R^{N_t\times M_t}$7 prediction modes. To enrich diversity, the framework expands the encoded feature $C\in\mathbb R^{N_t\times M_t}$8 into $C\in\mathbb R^{N_t\times M_t}$9 branches and applies a graph-based mode attention module (Wu et al., 19 Sep 2025). For each mode $X\in\{0,1\}^{N_t\times M_t}$0, a small graph is built whose nodes are the $X\in\{0,1\}^{N_t\times M_t}$1-step futures hypothesized for that mode. After flattening this graph, a standard multi-head GAT is applied: $X\in\{0,1\}^{N_t\times M_t}$2

The node update and attention coefficients are given as

$X\in\{0,1\}^{N_t\times M_t}$3

with

$X\in\{0,1\}^{N_t\times M_t}$4

In the stated interpretation, this module learns to up-weight the most plausible modes (Wu et al., 19 Sep 2025).

The framework uses $X\in\{0,1\}^{N_t\times M_t}$5 modes in the reported experiments (Wu et al., 19 Sep 2025). Evaluation metrics are explicitly defined with six modes: minADE is the minimum average $X\in\{0,1\}^{N_t\times M_t}$6 error over the best mode, minFDE is the minimum final-step $X\in\{0,1\}^{N_t\times M_t}$7 error, and MR is the miss rate under best-mode endpoint error $X\in\{0,1\}^{N_t\times M_t}$8 m (Wu et al., 19 Sep 2025). These definitions place CoPAD within the standard best-of-$X\in\{0,1\}^{N_t\times M_t}$9 multi-modal trajectory prediction paradigm.

Ablation results show that mode attention contributes an additional reduction in error beyond the PTA-equipped model. With Kalman-filter fusion, PTA, and two anchors, removing mode attention changes the reported metrics from minADE $$\min_{X}\;\sum_{i=1}^{N_t}\sum_{j=1}^{M_t} C_{ij}\,X_{ij}, \quad X\mathbf1 = \mathbf1,\; X^T\mathbf1 \le \mathbf1\,.$$0, minFDE $$\min_{X}\;\sum_{i=1}^{N_t}\sum_{j=1}^{M_t} C_{ij}\,X_{ij}, \quad X\mathbf1 = \mathbf1,\; X^T\mathbf1 \le \mathbf1\,.$$1, MR $$\min_{X}\;\sum_{i=1}^{N_t}\sum_{j=1}^{M_t} C_{ij}\,X_{ij}, \quad X\mathbf1 = \mathbf1,\; X^T\mathbf1 \le \mathbf1\,.$$2 to minADE $$\min_{X}\;\sum_{i=1}^{N_t}\sum_{j=1}^{M_t} C_{ij}\,X_{ij}, \quad X\mathbf1 = \mathbf1,\; X^T\mathbf1 \le \mathbf1\,.$$3, minFDE $$\min_{X}\;\sum_{i=1}^{N_t}\sum_{j=1}^{M_t} C_{ij}\,X_{ij}, \quad X\mathbf1 = \mathbf1,\; X^T\mathbf1 \le \mathbf1\,.$$4, MR $$\min_{X}\;\sum_{i=1}^{N_t}\sum_{j=1}^{M_t} C_{ij}\,X_{ij}, \quad X\mathbf1 = \mathbf1,\; X^T\mathbf1 \le \mathbf1\,.$$5 (Wu et al., 19 Sep 2025). The paper summarizes this as a reduction from $$\min_{X}\;\sum_{i=1}^{N_t}\sum_{j=1}^{M_t} C_{ij}\,X_{ij}, \quad X\mathbf1 = \mathbf1,\; X^T\mathbf1 \le \mathbf1\,.$$6 to $$\min_{X}\;\sum_{i=1}^{N_t}\sum_{j=1}^{M_t} C_{ij}\,X_{ij}, \quad X\mathbf1 = \mathbf1,\; X^T\mathbf1 \le \mathbf1\,.$$7 in minADE. While smaller than the PTA effect, it indicates that structured competition or reweighting among future modes remains beneficial.

5. Anchor-oriented decoder

The decoder in CoPAD is anchor-oriented and sparse. For each mode $$\min_{X}\;\sum_{i=1}^{N_t}\sum_{j=1}^{M_t} C_{ij}\,X_{ij}, \quad X\mathbf1 = \mathbf1,\; X^T\mathbf1 \le \mathbf1\,.$$8, the model defines two oriented anchors,

$$\min_{X}\;\sum_{i=1}^{N_t}\sum_{j=1}^{M_t} C_{ij}\,X_{ij}, \quad X\mathbf1 = \mathbf1,\; X^T\mathbf1 \le \mathbf1\,.$$9

with one anchor placed roughly near the midpoint and the other near the endpoint of a future trajectory (Wu et al., 19 Sep 2025). Let $$\mathcal T_{\rm matched} \;=\;\mathcal H(\mathcal T_V,\mathcal T_I), \quad \mathcal T_{\rm unmatched} \;=\;\bigl(\mathcal T_V\cup\mathcal T_I\bigr)\setminus\mathcal T_{\rm matched}.$$0 denote the final embedding for agent $$\mathcal T_{\rm matched} \;=\;\mathcal H(\mathcal T_V,\mathcal T_I), \quad \mathcal T_{\rm unmatched} \;=\;\bigl(\mathcal T_V\cup\mathcal T_I\bigr)\setminus\mathcal T_{\rm matched}.$$1. The decoder head for each mode is a small MLP, or alternatively an MLP-Mixer, that takes the concatenated input

$$\mathcal T_{\rm matched} \;=\;\mathcal H(\mathcal T_V,\mathcal T_I), \quad \mathcal T_{\rm unmatched} \;=\;\bigl(\mathcal T_V\cup\mathcal T_I\bigr)\setminus\mathcal T_{\rm matched}.$$2

and outputs the full future trajectory

$$\mathcal T_{\rm matched} \;=\;\mathcal H(\mathcal T_V,\mathcal T_I), \quad \mathcal T_{\rm unmatched} \;=\;\bigl(\mathcal T_V\cup\mathcal T_I\bigr)\setminus\mathcal T_{\rm matched}.$$3

Varying $$\mathcal T_{\rm matched} \;=\;\mathcal H(\mathcal T_V,\mathcal T_I), \quad \mathcal T_{\rm unmatched} \;=\;\bigl(\mathcal T_V\cup\mathcal T_I\bigr)\setminus\mathcal T_{\rm matched}.$$4 generates $$\mathcal T_{\rm matched} \;=\;\mathcal H(\mathcal T_V,\mathcal T_I), \quad \mathcal T_{\rm unmatched} \;=\;\bigl(\mathcal T_V\cup\mathcal T_I\bigr)\setminus\mathcal T_{\rm matched}.$$5 distinct trajectory hypotheses (Wu et al., 19 Sep 2025).

The paper characterizes the decoder as based on sparse anchors. In contrast to dense anchor parameterizations, the design uses only two anchors per mode. The reported ablation study compares different numbers of anchors per mode under Kalman-filter fusion, PTA, and mode attention. The results are:

Anchors per mode	minADE	minFDE	MR
0	1.27	2.08	0.32
1	1.26	2.06	0.32
2	1.24	2.00	0.29
3	1.25	2.03	0.31

The stated conclusion is that two anchors per mode is optimal and that more anchors do not help (Wu et al., 19 Sep 2025). This suggests that the decoder’s effectiveness depends less on anchor count than on a sparse geometric scaffold aligned with salient future positions.

6. Implementation profile and empirical results

The reported experimental setting uses a historical horizon $$\mathcal T_{\rm matched} \;=\;\mathcal H(\mathcal T_V,\mathcal T_I), \quad \mathcal T_{\rm unmatched} \;=\;\bigl(\mathcal T_V\cup\mathcal T_I\bigr)\setminus\mathcal T_{\rm matched}.$$6 s and a future horizon $$\mathcal T_{\rm matched} \;=\;\mathcal H(\mathcal T_V,\mathcal T_I), \quad \mathcal T_{\rm unmatched} \;=\;\bigl(\mathcal T_V\cup\mathcal T_I\bigr)\setminus\mathcal T_{\rm matched}.$$7 s, both sampled at $$\mathcal T_{\rm matched} \;=\;\mathcal H(\mathcal T_V,\mathcal T_I), \quad \mathcal T_{\rm unmatched} \;=\;\bigl(\mathcal T_V\cup\mathcal T_I\bigr)\setminus\mathcal T_{\rm matched}.$$8 Hz, corresponding to $$\mathcal T_{\rm matched} \;=\;\mathcal H(\mathcal T_V,\mathcal T_I), \quad \mathcal T_{\rm unmatched} \;=\;\bigl(\mathcal T_V\cup\mathcal T_I\bigr)\setminus\mathcal T_{\rm matched}.$$9 steps each (Wu et al., 19 Sep 2025). The PTA window is $\mathcal K$0, which is described as $\mathcal K$1 s back; the number of cross-attention heads is $\mathcal K$2, and the feature dimension is $\mathcal K$3 (Wu et al., 19 Sep 2025). The graph radius for agent–agent edges is approximately $\mathcal K$4 m. Optimization uses AdamW with initial learning rate $\mathcal K$5, weight decay $\mathcal K$6, cosine annealing, and dropout $\mathcal K$7. Training is reported for $\mathcal K$8 epochs on DAIR-V2X-Seq (Wu et al., 19 Sep 2025).

DAIR-V2X-Seq is described as a real-world V2X cooperative dataset with approximately $\mathcal K$9 ten-second sequences, each consisting of $$\mathcal T_{\rm fusion} \;=\; \mathcal K\bigl(\mathcal T_{\rm matched}\bigr)\;\cup\;\mathcal T_{\rm unmatched}\,.$$0 s history and $$\mathcal T_{\rm fusion} \;=\; \mathcal K\bigl(\mathcal T_{\rm matched}\bigr)\;\cup\;\mathcal T_{\rm unmatched}\,.$$1 s future, and covering vehicles, pedestrians, and detailed HD maps (Wu et al., 19 Sep 2025). This dataset serves as the benchmark for the reported cooperative trajectory prediction experiments.

The paper reports that CoPAD has approximately $$\mathcal T_{\rm fusion} \;=\; \mathcal K\bigl(\mathcal T_{\rm matched}\bigr)\;\cup\;\mathcal T_{\rm unmatched}\,.$$2 million trainable parameters, which is about $$\mathcal T_{\rm fusion} \;=\; \mathcal K\bigl(\mathcal T_{\rm matched}\bigr)\;\cup\;\mathcal T_{\rm unmatched}\,.$$3 of the $$\mathcal T_{\rm fusion} \;=\; \mathcal K\bigl(\mathcal T_{\rm matched}\bigr)\;\cup\;\mathcal T_{\rm unmatched}\,.$$4 million parameters in the previous V2X-Graph model (Wu et al., 19 Sep 2025). The quantitative comparison on DAIR-V2X-Seq with cooperative fusion on all models is:

Method	Params	minADE / minFDE / MR
TNT (coop)	0.5 M	7.38 / 15.27 / 0.72
laneGCN (coop)	1.0 M	1.45 / 2.96 / 0.41
DenseTNT (coop)	3.7 M	1.79 / 2.88 / 0.37
HiVT (coop)	2.6 M	1.29 / 2.43 / 0.35
V2X-Graph (coop)	5.0 M	1.17 / 2.03 / 0.29
CoPAD (coop)	3.2 M	1.24 / 2.00 / 0.29

The reported interpretation is that CoPAD achieves the state-of-the-art minFDE of $$\mathcal T_{\rm fusion} \;=\; \mathcal K\bigl(\mathcal T_{\rm matched}\bigr)\;\cup\;\mathcal T_{\rm unmatched}\,.$$5 m and ties the best MR of $$\mathcal T_{\rm fusion} \;=\; \mathcal K\bigl(\mathcal T_{\rm matched}\bigr)\;\cup\;\mathcal T_{\rm unmatched}\,.$$6, while using only $$\mathcal T_{\rm fusion} \;=\; \mathcal K\bigl(\mathcal T_{\rm matched}\bigr)\;\cup\;\mathcal T_{\rm unmatched}\,.$$7 of the parameters of V2X-Graph (Wu et al., 19 Sep 2025). The minADE is not the best in the table, since V2X-Graph reports $$\mathcal T_{\rm fusion} \;=\; \mathcal K\bigl(\mathcal T_{\rm matched}\bigr)\;\cup\;\mathcal T_{\rm unmatched}\,.$$8 versus CoPAD’s $$\mathcal T_{\rm fusion} \;=\; \mathcal K\bigl(\mathcal T_{\rm matched}\bigr)\;\cup\;\mathcal T_{\rm unmatched}\,.$$9. Accordingly, the contribution is not a uniform dominance across all metrics, but a specific trade-off combining strong final displacement accuracy, tied miss rate, and lower parameter count.

The paper also states that all models benefit substantially from cooperative fusion. For CoPAD specifically, minADE, minFDE, and MR improve by $\mathcal K$0, $\mathcal K$1, and $\mathcal K$2, respectively, relative to single-vehicle data (Wu et al., 19 Sep 2025). This supports the central V2X claim that cooperative sensing materially changes prediction quality rather than merely adding redundancy.

7. Interpretation, scope, and related design choices

CoPAD’s ablation structure emphasizes four coupled design choices: early raw-data fusion, a global temporal attention encoder, mode diversity attention, and a sparse anchor decoder (Wu et al., 19 Sep 2025). The paper’s summary attributes the reported state-of-the-art cooperative trajectory prediction result on DAIR-V2X-Seq to this combination. Within the evidence presented, PTA yields the largest gain, mode attention produces an additional but smaller gain, and two sparse anchors per mode outperform both fewer and more anchors (Wu et al., 19 Sep 2025).

A possible misconception is that cooperative trajectory prediction in V2X is primarily a matter of adding infrastructure features late in the pipeline. The reported ablation contradicts that interpretation: intermediate feature fusion by addition or concatenation performs worse than early fusion with Kalman filtering (Wu et al., 19 Sep 2025). Another possible misconception is that higher anchor count necessarily improves trajectory reconstruction. The reported decoder ablation does not support that; three anchors per mode is slightly worse than two (Wu et al., 19 Sep 2025).

The model is described as lightweight relative to V2X-Graph, but the available evidence should be interpreted narrowly. It supports a lower parameter count and better minFDE with tied MR on DAIR-V2X-Seq, not a universal superiority across all trajectory prediction metrics or datasets (Wu et al., 19 Sep 2025). Likewise, the framework’s design is tailored to V2X scenarios with access to vehicle and infrastructure trajectories. This suggests that its benefits are most directly relevant where cooperative sensing and communication are already present.

In the reported form, CoPAD represents a cooperative prediction architecture in which sensing incompleteness is addressed before sequence modeling, temporal interaction is handled through cross-frame attention, multi-modality is structured with a graph-based mode mechanism, and full trajectories are generated from sparse oriented anchors (Wu et al., 19 Sep 2025). Its empirical significance lies in showing that this particular combination can reach top-tier endpoint accuracy and miss rate on DAIR-V2X-Seq while remaining compact in parameter count.