Cross-LiDAR Alignment in Multi-Sensor SLAM

• Cross-LiDAR alignment is a set of techniques that enforce temporal consistency, motion alignment, and structural fidelity across LiDAR and cross-modal sensor data.
• It utilizes temporal embedding similarity, motion-aligned transformation loss, and windowed temporal fusion to minimize drift and boost mapping accuracy in SLAM.
• Domain-specific metrics, such as FVMD and correlation-peak distances, offer quantitative validation for improved performance in challenging, noisy sensing environments.

Cross-LiDAR alignment encompasses a collection of methodologies and architectural strategies that ensure the spatial and temporal consistency of LiDAR-based representations, particularly when fusing heterogenous sensor data or reconstructing LiDAR signals from cross-modal sources (e.g., radar, sonar). In the context of Simultaneous Localisation and Mapping (SLAM), robust cross-LiDAR alignment is central to minimizing drift, improving global map accuracy, and maintaining stable performance despite noisy or sparse measurements. Recent work exemplified by LiDAR-BIND-T (Balemans et al., 6 Sep 2025) advances this goal through mechanisms that enforce temporal consistency, motion-aligned alignment, and structural fidelity in the fused latent space, directly supporting both SLAM robustness and multi-sensor fusion.

1. Temporal Embedding Similarity

A core advance in LiDAR-BIND-T is the explicit enforcement of temporal proximity in latent embeddings. For consecutive sensor inputs at time $t$ and %%%%1%%%%, the model projects both into a shared latent space: $e_t$ and $e_{t-1}$. Temporal consistency is imposed via cosine similarity:

$$\mathcal{L}_\text{sim} = 1 - \frac{e_t \cdot e_{t-1}}{\|e_t\| \|e_{t-1}\|}$$

This loss penalizes abrupt changes in latent representations, encouraging smooth temporal evolution even when the inputs are subject to noise or sensor intermittency (as in radar or sonar). Maintaining such latent smoothness is critical in cross-modal fusion settings where transient disturbances may otherwise disrupt downstream data associations, scan matching, or trajectory estimation.

2. Motion-Aligned Transformation Loss

To align not only spatial features but also the inter-frame motion fields crucial for SLAM, the model introduces a transformation consistency loss. For predictions $(p_t, p_{t-1})$ and ground truth $(l_t, l_{t-1})$, it calculates the 2D cross-correlation maps $C(p_t, p_{t-1})$ and $C(l_t, l_{t-1})$. These are converted to probability distributions over displacement using a separable 2D softmax, yielding $Q_p$ and $Q_l$. The transformation loss is defined as:

$\mathcal{L}_T = D_\mathrm{KL}(Q_l \parallel Q_p)$

where $D_\mathrm{KL}$ is the Kullback–Leibler divergence. By minimizing this divergence, the model enforces that the predicted displacement distribution mirrors true LiDAR motion, thus reinforcing geometric compatibility frame-to-frame and enhancing scan matching reliability in SLAM.

3. Windows Temporal Fusion

Temporal fusion is approached via a windowed strategy: rather than processing each frame in isolation, the model applies a sliding window of size $N$ over a sequence of latent embeddings. Within this window, a specialized temporal fusion module—such as a temporal convolution or temporal transformer—learns to aggregate contextual information and filter out ephemeral noise. This ensures that predictions at time $t$ are informed not only by the current measurement but also by temporally local context, which is indispensable for preserving consistency in fast-changing or ambiguous environments.

4. Model Architecture Adaptations for Structural Fidelity

LiDAR-BIND-T replaces fully connected (linear) layers with convolutional layers in the encoder, ensuring that local spatial relationships—especially those crucial for geometric map integrity—are maintained throughout the representation. Additionally, instead of patchifying the range-azimuth input for a vision transformer, the architecture uses convolutional embedding to preserve the spatial topology of the entire sensor field. These changes jointly promote spatial coherence in the output embeddings, which is a prerequisite for high-quality cross-LiDAR alignment and reliable spatial registration in multi-sensor SLAM pipelines.

5. Evaluation Metrics for Temporal and Spatial Consistency

Standard video metrics such as FVD or FID-VID do not adequately capture the characteristics of sparse, time-varying LiDAR data. LiDAR-BIND-T proposes domain-specific metrics:

Metric Name	Application	Interpretation
Fréchet Video Motion Distance (FVMD)	Temporal motion consistency	Lower FVMD → predicted motion matches ground truth
Correlation-Peak Distance Metric	Motion displacement, scan matching	Smaller peak distance → improved motion alignment
Absolute Trajectory Error, Map Occupancy	SLAM trajectory and occupancy accuracy	Lower error/higher IoU → better mapping

These metrics directly quantify the impact of alignment mechanisms on the utility of reconstructions for robotic mapping and navigation, transcending framewise fidelity and focusing on the preservation of trajectory and occupancy structure essential for SLAM.

6. Impact on SLAM Systems

The combination of temporally aligned embeddings, motion-consistent predictions, and windowed fusion substantially raises the temporal and spatial coherence of generated LiDAR representations. Empirical results demonstrate benefits including:

• Reduced absolute trajectory error (lower drift over long navigation episodes).
• Increased occupancy map accuracy (IoU) in Cartographer-based SLAM.
• Improved robustness to sensor noise and cross-modal translation errors.
• Enhanced scan matching via better-aligned framewise motion and structural details.

Such improvements are critical in real-world autonomous navigation where cross-modal fusion is employed to compensate for missing or unreliable LiDAR data.

Conclusion

Cross-LiDAR alignment as operationalized in LiDAR-BIND-T (Balemans et al., 6 Sep 2025) constitutes a comprehensive strategy that couples temporal embedding similarity, motion-aligned optimization, and dedicated architectural design. These mechanisms collectively address the fundamental need for temporally and spatially robust LiDAR alignment in multi-sensor SLAM and reconstruction. Domain-specific metrics such as FVMD and correlation-peak distances provide practical evaluation tools that correlate improvements in representation consistency with tangible enhancements in SLAM performance. The result is an architecture that substantially elevates the plug-and-play fusion of cross-modal signals, yielding reliable, temporally stable outputs for downstream localisation and mapping.