Learned Memory Attenuation in Sage-Husa Kalman Filters for Robust UAV State Estimation

Problem
This paper addresses the limitations of classical Kalman filters, particularly in the context of Unmanned Aerial Vehicles (UAVs) operating in dynamic environments. Traditional Kalman filters assume stationary noise characteristics, which are often invalidated by telemetry outages, structural vibrations, and regime-dependent noise. The Sage-Husa Kalman Filter (SHKF) improves upon this by estimating noise statistics online but is constrained by a static scalar forgetting factor. This leads to a trade-off between steady-state stability and transient responsiveness. The authors propose a novel approach to overcome these limitations by introducing a learned memory attenuation mechanism, which is not covered in existing literature. This work is presented as a preprint and has not yet undergone peer review.

Method
The core technical contribution is the N-Deep Recurrent Sage-Husa Filter (NDR-SHKF), which replaces the static scalar forgetting factor with a vector-valued memory attenuation policy. This policy is learned using a hierarchical recurrent neural network that processes whitened innovation sequences. The architecture is bifurcated: shallow recurrent states are designed to capture instantaneous sensor anomalies, while deep recurrent states encode sustained dynamic trends. An auxiliary reconstruction objective is employed to prevent feature collapse during training. The entire filter, including recursive covariance updates, is trained end-to-end using backpropagation through time, with the objective of minimizing state estimation error directly.

Results
The NDR-SHKF was evaluated on topologically distinct chaotic attractors, demonstrating significant cross-domain generalization. It outperformed purely data-driven baselines, which exhibited divergence under out-of-distribution dynamics. In practical evaluations on real-world UAV flight datasets, the NDR-SHKF effectively bridged transitions into proprioceptive dead reckoning and surpassed classical adaptive estimators during sensor outages. Specific performance metrics were not disclosed in the abstract, but the results indicate a robust improvement over existing methods in challenging conditions.

Limitations
The authors acknowledge that the reliance on a learned memory attenuation policy may introduce additional complexity and potential overfitting, particularly in scenarios with limited training data. They do not discuss the computational overhead associated with the hierarchical recurrent architecture or the implications of real-time deployment in resource-constrained UAV systems. Additionally, the generalizability of the learned policy across diverse UAV platforms and environments remains to be fully validated.

Why it matters
This work has significant implications for the field of state estimation in UAVs, particularly in environments characterized by dynamic and unpredictable conditions. By integrating learned memory attenuation into the Kalman filtering framework, the NDR-SHKF offers a promising avenue for enhancing robustness and adaptability in state estimation tasks. This could lead to improved performance in various applications, including autonomous navigation, surveillance, and search-and-rescue operations, where reliable state estimation is critical.

Authors: Kenan Majewski, Marcin Żugaj
Source: arXiv:2605.18704
URL: https://arxiv.org/abs/2605.18704v1