Tensor Decompositions for Online Grid-Based Terrain-Aided Navigation
J. Matou\v{s}ek, J. Krej\v{c}\'i, J. Dun\'ik, and R. Zanetti

TL;DR
This paper introduces a scalable grid-based state estimation method using tensor decompositions for high-dimensional models with non-linear measurements, enabling real-time terrain-aided navigation and applicable to various decomposable models.
Contribution
It presents a practical tensor decomposition-based filtering approach that exploits model structure for efficient high-dimensional state estimation, extending grid-based filters' applicability.
Findings
Enables real-time estimation in high-dimensional models.
Uses low-rank tensor decompositions for efficient state density propagation.
Demonstrates effectiveness in terrain-aided navigation scenarios.
Abstract
This paper presents a practical and scalable grid-based state estimation method for high-dimensional models with invertible linear dynamics and with highly non-linear measurements, such as the nearly constant velocity model with measurements of e.g. altitude, bearing, and/or range. Unlike previous tensor decomposition-based approaches, which have largely remained at the proof-of-concept stage, the proposed method delivers an efficient and practical solution by exploiting decomposable model structure-specifically, block-diagonal dynamics and sparsely coupled measurement dimensions. The algorithm integrates a Lagrangian formulation for the time update and leverages low-rank tensor decompositions to compactly represent and effectively propagate state densities. This enables real-time estimation for models with large state dimension, significantly extending the practical reach of grid-based…
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Taxonomy
TopicsTensor decomposition and applications · Model Reduction and Neural Networks · Aerospace and Aviation Technology
