Radar Odometry Subject to High Tilt Dynamics of Subarctic Environments

1. Problem Statement

Rotating Frequency Modulated Continuous Wave (FMCW) radar odometry systems currently rely heavily on the assumption of flat ground. While this works well in urban or flat mining environments, it fails in subarctic and dynamic terrains where vehicles experience significant and rapid changes in orientation (pitch and roll).

• The Challenge: Standard feature extraction and state estimation techniques struggle when consecutive radar scans differ by up to 13° in pitch and 4° in roll, with absolute attitudes reaching 30° pitch and 8° roll.
• Limitations of Existing Methods: Current state-of-the-art (SOTA) methods (e.g., CFEAR, ORORA, RT&R) often fail in these conditions because:
  • They rely on single-axis orientation priors (e.g., assuming the IMU's vertical axis is the only rotation axis), which breaks down during complex vehicle tilts.
  • They suffer from data association failures due to altered geometric observations between scans.
  • They struggle with lateral slip and steep terrain features (e.g., ditches, stone quarries).

2. Methodology

The authors propose a novel Radar-Inertial Odometry method that integrates IMU data with radar point clouds to handle high-dynamic tilt. The pipeline (illustrated in Figure 2 of the paper) consists of the following stages:

• IMU Processing: Raw IMU data (200 Hz) is bias-corrected and fed into a Madgwick filter to estimate the vehicle's 3D orientation ($q \in \mathbb{H}$).
• Tilt-Proximity Submap Search: Instead of a simple spatial search, the system searches for reference submaps based on:
  • Spatial proximity ($r_{submap}$).
  • Tilt proximity: The pitch and roll difference between the current scan and the submap must be below a threshold ($\tau_{tilt}$).
  • If no matching submap is found, the system conservatively resets the estimated velocity to zero.
• Radar Feature Extraction:
  • Raw polar intensity images are processed using the k-strongest approach to extract high-intensity peaks.
  • 3D Deskewing: Motion compensation is applied using spherical linear interpolation of orientation data.
• Tilt-Based Filtering (Core Innovation):
  • A hard threshold filter is applied to the deskewed point cloud.
  • It calculates the vertical distance ($\Delta d$) between each point and an estimated axis of rotation derived from the relative quaternion.
  • Points are weighted using a Cauchy function based on this distance.
  • A hard threshold ($\tau_{tilt}$) removes points that are too far from the rotation axis, effectively filtering out noise caused by vehicle tilt and ground irregularities.
• Registration: The filtered point cloud is matched to the reference submap using Point-to-Point Iterative Closest Point (ICP). A constant velocity model and estimated yaw angle serve as priors.

3. Key Contributions

1. Tilt-Proximity Submap Search: A novel search strategy for ICP reference maps that accounts for vehicle orientation (pitch/roll) rather than just spatial distance.
2. Cauchy-Based Hard Threshold Filter: A filtering mechanism that weights and removes points based on their vertical displacement relative to the estimated rotation axis, improving robustness against dynamic tilt.
3. Comprehensive Benchmarking: An evaluation of the proposed method against three SOTA radar odometry methods (CFEAR, ORORA, RT&R) on the Forêt Montmorency (FoMo) dataset, which includes challenging subarctic conditions (snow, ditches, steep slopes).

4. Experimental Results

The methods were tested on two trajectories from the FoMo dataset:

• Red Loop (Urban Baseline): 300m flat, paved circuit.
• Orange Loop (Dynamic Subarctic): 2km trajectory featuring a stone quarry, steep downhill/uphill sections, a ditch traversal, and forest corridors with up to 1m of snow accumulation.

Performance Metrics (Relative Translation Error - RTE):

• Urban Baseline: The proposed method achieved State-of-the-Art (SOTA) performance, comparable to the best existing methods.
• Dynamic Subarctic Trajectory:
  • The proposed method achieved a 0.3% improvement over the second-best method (CFEAR).
  • Median RTE: The proposed method maintained a median error of 2.8% on the dynamic loop, compared to CFEAR's 3.1%.
  • Failure Rates: RT&R failed in 2 out of 9 runs on the dynamic trajectory due to high tilt differences. ORORA and RT&R suffered from incorrect heading estimations in steep sections.
• Specific Scenarios:
  • Ditch Traversal: The proposed method showed smaller deviation than CFEAR and recovered orientation more accurately after high lateral slip.
  • Snow Corridors: While all methods struggled with the "corridor effect" caused by snowbanks, the proposed method successfully completed the loop where others diverged significantly from the Ground Truth.

5. Significance and Future Work

• Significance: This work demonstrates that rotating FMCW radar odometry can be robust in highly dynamic, non-flat environments (subarctic/mining) by explicitly modeling vehicle tilt and filtering points based on rotation axes. It bridges the gap between urban radar odometry and the harsh realities of off-road navigation.
• Future Work:
  • Incorporating translational priors into the motion compensation module.
  • Conducting ablation studies to isolate the impact of tilt-based filtering vs. submap search.
  • Integrating dense radar odometry methods into the benchmark suite.
  • Validating the framework on large-scale standard urban driving datasets.

In conclusion, the paper establishes a new benchmark for radar odometry in extreme conditions, proving that combining inertial data with tilt-aware geometric filtering significantly outperforms current solutions in subarctic and dynamic terrains.