Attention-Based Neural-Augmented Kalman Filter for Legged Robot State Estimation

Seokju Lee, Kyung-Soo Kim
Mechatronics, Systems and Control Lab, Korea Advanced Institute of Science and Technology (KAIST)
IEEE Robotics and Automation Letters (RA-L)
IEEE Xplore arXiv

Supplementary Video of the Paper

Abstract

In this letter, we propose an Attention-Based Neural-Augmented Kalman Filter (AttenNKF) for state estimation in legged robots. Foot slip is a major source of estimation error: when slip occurs, kinematic measurements violate the no-slip assumption and inject bias during the update step. Our objective is to estimate this slip-induced error and compensate for it. To this end, we augment an Invariant Extended Kalman Filter (InEKF) with a neural compensator that uses an attention mechanism to infer error conditioned on foot-slip severity and then applies this estimate as a post-update compensation to the InEKF state (i.e., after the filter update). The compensator is trained in a latent space, which aims to reduce sensitivity to raw input scales and encourages structured slip-conditioned compensations, while preserving the InEKF recursion. Experiments demonstrate improved performance compared to existing legged-robot state estimators, particularly under slip-prone conditions.

Method: Slip as Context

Overall Architecture

AttenNKF Architecture
Figure 1. Structure of the AttenNKF. The system augments a standard InEKF with a Neural Compensator (NC). Unlike traditional methods that simply concatenate inputs, our NC uses an Attention Mechanism where the Foot Slip Level acts as a context (Query) to modulate the InEKF State History (Key/Value).


Training Process

Training Process
Figure 2. Training pipeline of the Neural Compensator. The training consists of two stages:
  • Step 1 (Autoencoder): Compresses the Foot Slip Level, InEKF State, and Error into latent spaces using GRU-based autoencoders.
  • Step 2 (Attention): Trains the Cross-Attention module. The Slip Latent is used as the Query, while the InEKF Latent provides Keys and Values. This generates a slip-conditioned compensation latent vector.

Experimental Setup

Experimental Environment
Figure 3. Real-world indoor experimental environment. The setup includes: (1) a Gravel field (30mm pebbles) to induce noise, (2) a Teflon sheet ($\mu \approx 0.15$) to simulate ice-like slippery surfaces, and (3) Stairs for dynamic locomotion tests.

Experimental Environments & Trajectory

We evaluated the proposed method across various terrain conditions.
The experiments cover nominal walking, slippery/noisy surfaces, and long-term trajectory tracking.

Full Trajectory

Indoor trajectory

Flat Ground

Nominal walking

Gravel Field

Noisy surface (30mm pebbles)

Teflon Sheet

Slippery surface ($\mu \approx 0.15$)

Stairs

Uneven terrain

Soft Terrain

Deformable surface (OOD)



Quantitative Results

Indoor Experimental Results
RMSE Comparison Table
Figure 4 & Table 1. State estimation performance. (Left) Trajectories and state histories comparing AttenNKF with baselines. (Right) RMSE comparison table showing that AttenNKF achieves the lowest drift, particularly in slippery and noisy conditions.

Outdoor Experiment

The robot traversed approximately 100m on deformable grass terrain. While baselines accumulated up to 10m of vertical drift, AttenNKF maintained errors within $\pm 2-3$m.

Outdoor Experimental Results
Figure 5. Outdoor experiment results. Top: Trajectory overlaid on a satellite map. Bottom: Estimated vertical position ($z$) over time.

BibTeX

@ARTICLE{11393905,
  author={Lee, Seokju and Kim, Kyung-Soo},
  journal={IEEE Robotics and Automation Letters}, 
  title={Attention-Based Neural-Augmented Kalman Filter for Legged Robot State Estimation}, 
  year={2026},
  volume={11},
  number={4},
  pages={4122-4129},
  keywords={Foot;Robot sensing systems;State estimation;Legged locomotion;Kalman filters;Kinematics;History;Noise;Correlation;Neural networks;Legged robots;proprioceptive state estimation;attention mechanisms},
  doi={10.1109/LRA.2026.3664311}}