High-Precision Autonomous Positioning of an Unmanned Locomotive Based on the Integration of a Kolmogorov — Arnold Network with an Extended Kalman Filter

Kirill Evdokimov; Sergey Sokolov; Dmitriy Shvalov; Vladislav Kamenskiy

doi:10.20295/2412-9186-2026-12-03-169-181

UDC 629.4.052.9 UDC 004.8

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HIGH-PRECISION AUTONOMOUS POSITIONING OF AN UNMANNED LOCOMOTIVE BASED ON THE INTEGRATION OF A KOLMOGOROV — ARNOLD NETWORK WITH AN EXTENDED KALMAN FILTER High-Precision Autonomous Positioning of an Unmanned Locomotive Based on the Integration of a Kolmogorov — Arnold Network with an Extended Kalman Filter

АА Аа

Published in Transport automation research · Volume 12, Issue 3, 2026 · Pages 169–181 · Rubric: VIABILITY, RELIABILITY, SAFETY

DOI: https://doi.org/10.20295/2412-9186-2026-12-03-169-181

Received: 16.09.2026 Accepted: 20.09.2026 Published: 20.09.2026

Authors

Kirill Evdokimov

Sergey Sokolov

Dmitriy Shvalov

Vladislav Kamenskiy

Kirill Evdokimov

Rostov State Transport University Postgraduate Student · “Automation and Remote Control on Railways” Department · Russian Federation

Sergey Sokolov

Academic degree: doctor of technical sciences

Science rang: professor

Rostov State University of Economics Professor · Information Technologies and Information Protection Department · Rostov-on-Don

Moscow State Technical University of Communications and Informatics, North Caucasus Branch “Informatics and Computer Science” Department · Russian Federation

Dmitriy Shvalov

Academic degree: candidate of technical sciences

Science rang: docent

Rostov State University of Means of Communication “Railway Automation and Remote Control” Department · Rostov-on-Don

Vladislav Kamenskiy

Academic degree: candidate of technical sciences

Science rang: docent

Rostov State Transport University “Automation and Remote Control on Railways” Department · Russian Federation

ABSTRACT

the paper considers the problem of improving the accuracy of autonomous navigation-parameter estimation for an unmanned locomotive under unavailable or limited satellite positioning. A positioning algorithm based on the integration of an extended Kalman filter and a Kolmogorov — Arnold network is proposed. The extended Kalman filter estimates the travelled distance and velocity using a nonlinear model of longitudinal locomotive motion and measurements from autonomous sensors. The KAN module generates a predictive state estimate taking into account the track gradient and curvature. The scientific novelty consists in using the neural-network prediction to form an additional a priori estimate and in introducing a prediction-error covariance determined from validation data. The algorithm is studied by simulation under measurement noise, wheelset slip, short-term measurement outages, random longitudinal accelerations, variable gradient, and track curvature. The Railway-Precise-Localization dataset, containing precise GNSS/RTK and IMU measurements recorded onboard a railway vehicle, is used to form a reference railway trajectory. If standard odometer and tachometer channels are absent from the selected data, their measurements are generated by adding prescribed errors to the reference distance and velocity. The results demonstrate a reduction in position and velocity root-mean-square errors compared with a conventional extended Kalman filter. The results characterize the performance of the method within the domain represented in the training data and require additional validation on independent routes with different dynamic and geometrical characteristics.

KEYWORDS

unmanned locomotive, autonomous positioning, state-vector estimation, extended Kalman filter, neural-network prediction, predictive state estimation, Kolmogorov — Arnold network, KAN, odometry, railway navigation

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GOST

Evdokimov K. A., Sokolov S. V., Shvalov D. V., Kamenskiy V. V. High-Precision Autonomous Positioning of an Unmanned Locomotive Based on the Integration of a Kolmogorov — Arnold Network with an Extended Kalman Filter // Transport automation research. 2026. no. 3. pp. 169-181. DOI: https://doi.org/10.20295/2412-9186-2026-12-03-169-181. (Date of access 20.09.2026).

MLA

Kirill Evdokimov, Sokolov S. V., Shvalov D. V., Kamenskiy V. V.. "High-Precision Autonomous Positioning of an Unmanned Locomotive Based on the Integration of a Kolmogorov — Arnold Network with an Extended Kalman Filter." Transport automation research 12.3 (2026): 169-181. DOI: https://doi.org/10.20295/2412-9186-2026-12-03-169-181.

APA

Evdokimov K. A., Sokolov S. V., Shvalov D. V., Kamenskiy V. V. (2026). High-Precision Autonomous Positioning of an Unmanned Locomotive Based on the Integration of a Kolmogorov — Arnold Network with an Extended Kalman Filter. Transport automation research, 12(3), 169-181. https://doi.org/10.20295/2412-9186-2026-12-03-169-181

Chicago

Kirill Evdokimov, Sokolov S. V., Shvalov D. V., Kamenskiy V. V.. "High-Precision Autonomous Positioning of an Unmanned Locomotive Based on the Integration of a Kolmogorov — Arnold Network with an Extended Kalman Filter." Transport automation research 12, no. 3 (2026): 169-181. https://doi.org/10.20295/2412-9186-2026-12-03-169-181.

WIKI

{{cite journal | author = Evdokimov K. A., Sokolov S. V., Shvalov D. V., Kamenskiy V. V. | title = High-Precision Autonomous Positioning of an Unmanned Locomotive Based on the Integration of a Kolmogorov — Arnold Network with an Extended Kalman Filter | journal = Transport automation research | year = 2026 | volume = 12 | issue = 3 | pages = 169-181 | doi = 10.20295/2412-9186-2026-12-03-169-181 }}

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