A Proprioceptive-Only Benchmark for Quadruped State Estimation: ATE, RPE, and Runtime Trade-offs Between Filters and Smoothers

2026-05-12

AI Summary

This study addresses the problem of state estimation for quadrupedal robots under purely proprioceptive conditions by presenting the first fair and reproducible comparative evaluation of MUSE, the Invariant Extended Kalman Filter (IEKF), and the Invariant Smoother (IS) on a unified hardware-software platform. Leveraging the CYN-1 sequence from the GrandTour dataset, the authors systematically assess the accuracy and computational efficiency of these methods using metrics including Absolute Trajectory Error (ATE), Relative Pose Error (RPE), and per-update runtime. The results demonstrate that IEKF and IS achieve significantly lower ATE than MUSE, while all three exhibit comparable RPE, revealing a clear trade-off between estimation accuracy and latency. The complete implementation and documentation are open-sourced to support informed algorithm selection for real-world deployment.

Abstract

We compare three state-of-the-art proprioceptive state estimators for quadruped robots: MUSE [1], the Invariant Extended Kalman Filter (IEKF) [2], and the Invariant Smoother (IS) [3], on the CYN-1 sequence of the GrandTour Dataset [4]. Our goal is to give practitioners clear guidance on accuracy and computation time: we report long-term accuracy (Absolute Trajectory Error, ATE), short-term accuracy (translational and rotational Relative Pose Error, RPE), and per-update computation time on a fixed hardware/software stack. On this dataset, RPEs are broadly similar across methods, while IEKF and IS achieve a lower ATE than MUSE. Runtime results highlight the accuracy-latency trade-offs across the three approaches. In the discussion, we outline the evaluation choices used to ensure a fair comparison and analyze factors that influence short-horizon metrics. Overall, this study provides a concise snapshot of accuracy and cost, helping readers choose an estimator that fits their application constraints, with all evaluation code and documentation released open-source at https://github.com/iit-DLSLab/state_estimation_benchmark for full reproducibility.

Problem

• quadruped
• state estimation
• proprioceptive
• ATE
• RPE

Innovation

• proprioceptive-only benchmark
• quadruped state estimation
• accuracy-latency trade-off
• Invariant Extended Kalman Filter
• open-source evaluation