Tensor Decompositions for Online Grid-Based Terrain-Aided Navigation

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 filters beyond their traditional low-dimensional use. Although demonstrated in the context of terrain-aided navigation, the method is applicable to a wide range of models with decomposable structure. The computational complexity and estimation accuracy depend on the specific structure of the model. All experiments are fully reproducible, with source code provided alongside this paper (GitHub link: https://github.com/pesslovany/Matlab-LagrangianPMF).