How to Interpret ATE, RPE, and AUC Metrics for Trajectory Evaluation in LingBot-Map

LingBot-Map evaluates camera trajectory accuracy using three complementary metrics—Absolute Trajectory Error (ATE), Relative Pose Error (RPE), and Area Under the Curve (AUC)—computed via the Evo library after Sim(3) alignment to measure global drift, local consistency, and robustness within error thresholds.

Understanding how to interpret ATE, RPE, and AUC metrics for trajectory evaluation in LingBot-Map is essential for benchmarking visual SLAM systems. The Robbyant/lingbot-map repository provides a standardized evaluation pipeline that quantifies camera pose estimation accuracy through these three core statistics. These metrics are calculated after applying a Sim(3) similarity transform to align estimated and ground-truth trajectories, ensuring fair comparison across different reconstruction scales.

What Are ATE, RPE, and AUC?

The LingBot-Map benchmark employs these metrics to quantify distinct aspects of trajectory accuracy:

Absolute Trajectory Error (ATE)

ATE measures the root-mean-square distance between estimated camera positions and ground-truth positions after aligning the entire trajectory with a scale-aware similarity transform. Low ATE indicates the global pose estimate closely follows the true path, while high ATE signals accumulated drift over the sequence. The result is stored under the key traj.ate in the manifest builder (benchmark/benchmark/report/manifest_builder.py).

Relative Pose Error (RPE)

RPE evaluates the error between successive poses (or over a short window) after removing global alignment. It combines translation and rotation components to assess local consistency. Low RPE means local motion preserves geometry without jitter, whereas high RPE indicates inconsistent motion estimation even when global alignment appears correct. These values are reported as traj.rpe_trans and traj.rpe_rot.

Area Under the Curve (AUC)

AUC computes the integral of the cumulative distribution of ATE values up to specified thresholds (typically 0.05 m, 0.1 m, and 0.2 m). Larger AUC values (closer to 1.0) indicate a higher proportion of trajectory samples remain within tolerable error bounds, reflecting system robustness. The implementation calculates both traj.auc_micro and traj.auc_macro scores.

How LingBot-Map Computes Trajectory Metrics

The evaluation pipeline follows a three-stage process implemented across specific modules:

1. Trajectory Loading: The module benchmark/benchmark/io/trajectory.py parses ground-truth and estimated pose files in TUM or Euroc format.

2. Metric Calculation: The benchmark/benchmark/evaluation/trajectory.py file invokes the Evo library (evo.core) through the function evaluate_trajectory(). This returns a dictionary containing ate, rpe_trans, and rpe_rot after applying Sim(3) alignment (scale, rotation, and translation).

3. AUC Evaluation: The benchmark/benchmark/evaluation/auc.py module calculates the area under the curve using compute_auc(), aggregating results under the micro and macro keys mentioned above.

This Sim(3) alignment ensures metrics reflect reconstruction quality rather than raw sensor output, enabling fair comparison between different SLAM pipelines on the same dataset.

Interpreting Evaluation Results

When analyzing LingBot-Map output:

• ATE values below 0.05 m indicate excellent global accuracy, while values above 0.1 m suggest significant drift.
• RPE translation errors below 0.01 m per segment indicate consistent local motion without jitter.
• AUC scores approaching 1.0 for the 0.2 m threshold demonstrate that most frames stay within acceptable error bounds.

High ATE with low RPE suggests accurate local tracking but poor global consistency (e.g., loop closure failures). Conversely, low ATE with high RPE indicates good global alignment but noisy local estimates.

Practical Implementation Example

The following implementation mirrors the benchmark runner in benchmark/evaluate.py:

from benchmark.benchmark.io import trajectory as traj_io
from benchmark.benchmark.evaluation import trajectory as traj_eval
from benchmark.benchmark.evaluation import auc as auc_eval

# Load ground-truth and estimate (TUM format)

gt = traj_io.load_trajectory("data/groundtruth.tum")
est = traj_io.load_trajectory("output/estimated.tum")

# Compute ATE and RPE after Sim(3) alignment

metrics = traj_eval.evaluate_trajectory(gt, est)
print(f"ATE = {metrics['ate']:.3f} m")
print(f"RPE_trans = {metrics['rpe_trans']:.3f} m")
print(f"RPE_rot = {metrics['rpe_rot']:.2f} deg")

# Compute AUC for standard thresholds

thresholds = [0.05, 0.1, 0.2]   # meters

auc_results = auc_eval.compute_auc(metrics['ate_errors'], thresholds)
print(f"AUC (≤0.2 m) = {auc_results[-1]:.3f}")

This code produces the exact values reported in LingBot-Map evaluation tables, utilizing the same Evo library calls found in the source.

Summary

• ATE quantifies global trajectory accuracy via root-mean-square error after Sim(3) alignment, stored in traj.ate.
• RPE measures local consistency through relative pose errors, accessible via traj.rpe_trans and traj.rpe_rot in the evaluation output.
• AUC summarizes robustness by calculating the cumulative distribution of ATE errors up to thresholds, reported as traj.auc_micro and traj.auc_macro.
• The evaluation pipeline relies on the Evo library within benchmark/benchmark/evaluation/trajectory.py and benchmark/benchmark/evaluation/auc.py.
• All metrics require Sim(3) alignment to ensure scale-aware comparison between estimated and ground-truth trajectories.

Frequently Asked Questions

What is considered a good ATE value in LingBot-Map?

A good ATE value is typically below 0.05 meters, indicating minimal global drift. Values between 0.05 m and 0.1 m represent moderate accuracy, while anything above 0.1 m suggests significant accumulated error in the trajectory estimation that may require loop closure optimization.

How does Sim(3) alignment affect the trajectory metrics?

Sim(3) alignment applies a similarity transform (scale, rotation, and translation) to the estimated trajectory before computing errors. This removes scale ambiguity and global offset, ensuring that ATE and RPE reflect the actual reconstruction quality rather than initialization differences or metric scale discrepancies between the estimated and ground-truth paths.

Why does LingBot-Map use both ATE and RPE metrics?

ATE and RPE provide complementary information: ATE reveals global drift and loop closure success, while RPE exposes local tracking consistency and jitter. A system might achieve low ATE through aggressive global optimization yet suffer from high RPE due to noisy frame-to-frame estimates, making both metrics necessary for comprehensive evaluation of SLAM performance.

How is AUC calculated in the LingBot-Map benchmark?

AUC is computed in benchmark/benchmark/evaluation/auc.py by integrating the cumulative distribution function of ATE errors across specified thresholds (0.05 m, 0.1 m, 0.2 m). The result represents the proportion of pose estimates falling within each error bound, with higher values indicating greater robustness throughout the sequence.

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