Visual-inertial navigation of UAVs with adaptive uncertainty estimation of neural network localization based on evidential learning

Visual-inertial navigation of UAVs with adaptive uncertainty estimation of neural network localization based on evidential learning

Lazareva P.A. (KAI, Kazan, Russia)
Gurko N.V. (KAI, Kazan, Russia)

Abstract

This paper addresses the problem of visual–inertial navigation for unmanned aerial vehicles operating in GNSS-denied environments. An adaptive approach to estimating the measurement covariance of a neural-network-based absolute visual localization module is proposed. The method is based on Evidential Deep Learning (EDL) with a Normal–Inverse Gamma parameterization. The concept of the degree of explainable observability is introduced as a context-dependent quantitative measure of the informativeness of absolute measurements. A theorem is proved demonstrating observability degeneration under the conventional process covariance formulation, and a modified process covariance is proposed to maintain a non-zero Kalman gain between absolute measurement updates. A systematic experimental study is conducted, including four adaptive measurement covariance formulations, two process covariance modes, and an automatic strategy-switching algorithm evaluated on two synthetic datasets and one real flight dataset. The evidential covariance consistently outperforms the heuristic baseline across all three datasets, with performance gains increasing monotonically with scene informativeness. Specifically, the average trajectory error is reduced by 7–46% compared with the heuristic approach. On the most informative dataset, the proposed method achieves a 46% reduction in trajectory error while increasing the proportion of accurately localized frames from 27% to 66%. The modified process covariance improves the Kalman gain in scenarios where drift accumulates between absolute updates. Finally, an analysis of the method's applicability shows that its performance gain is governed by the correlation between the error predicted by the EDL model and the actual localization error, providing a quantitative criterion for assessing the applicability of the proposed approach.

Keywords

unmanned aerial vehicle; visual-inertial navigation; error state Kalman filter; absolute visual localization; neural network descriptor; explainable artificial intelligence; deep learning; epistemic uncertainty.

Edition

Proceedings of the Institute for System Programming, vol. 38, issue 4, part 1, 2026, pp. 239-256

ISSN 2220-6426 (Online), ISSN 2079-8156 (Print).

DOI: 10.15514/ISPRAS-2026-38(4)-13

For citation

Lazareva P.A., Gurko N.V. Visual-inertial navigation of UAVs with adaptive uncertainty estimation of neural network localization based on evidential learning. Proceedings of the Institute for System Programming, vol. 38, issue 4, part 1, 2026, pp. 239-256 DOI: 10.15514/ISPRAS-2026-38(4)-13.

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