Spatially scalable recursive estimation of Gaussian process terrain maps using local basis functions

• URL: http://arxiv.org/abs/2210.09168v2
• Date: Sun, 3 Dec 2023 13:59:13 GMT
• Title: Spatially scalable recursive estimation of Gaussian process terrain maps using local basis functions
• Authors: Frida Marie Viset, Rudy Helmons and Manon Kok
• Abstract summary: Online mapping of nonlinear terrains can be used to improve position estimates when an agent returns to a previously mapped area. GP mapping algorithms have increasing computational demands as the mapped area expands. We show experimentally that our algorithm is faster than existing methods when the mapped area is large.
• Score: 0.9208007322096532
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: When an agent, person, vehicle or robot is moving through an unknown environment without GNSS signals, online mapping of nonlinear terrains can be used to improve position estimates when the agent returns to a previously mapped area. Mapping algorithms using online Gaussian process (GP) regression are commonly integrated in algorithms for simultaneous localisation and mapping (SLAM). However, GP mapping algorithms have increasing computational demands as the mapped area expands relative to spatial field variations. This is due to the need for estimating an increasing amount of map parameters as the area of the map grows. Contrary to this, we propose a recursive GP mapping estimation algorithm which uses local basis functions in an information filter to achieve spatial scalability. Our proposed approximation employs a global grid of finite support basis functions but restricts computations to a localized subset around each prediction point. As our proposed algorithm is recursive, it can naturally be incorporated into existing algorithms that uses Gaussian process maps for SLAM. Incorporating our proposed algorithm into an extended Kalman filter (EKF) for magnetic field SLAM reduces the overall computational complexity of the algorithm. We show experimentally that our algorithm is faster than existing methods when the mapped area is large and the map is based on many measurements, both for recursive mapping tasks and for magnetic field SLAM.

Related papers

• Approximating Metric Magnitude of Point Sets [4.522729058300309]
  Metric magnitude is a measure of the "size" of point clouds with many desirable geometric properties. It has been adapted to various mathematical contexts and recent work suggests that it can enhance machine learning and optimization algorithms. In this paper, we study the magnitude problem, and show efficient ways of approximating it. We show that it can be cast as a convex optimization problem, but not as a submodular optimization. The paper describes two new algorithms - an iterative approximation algorithm that converges fast and is accurate, and a subset selection method that makes the computation even faster.
  arXiv  Detail & Related papers  (2024-09-06T17:15:28Z)
• Large-scale magnetic field maps using structured kernel interpolation for Gaussian process regression [0.9208007322096532]
  We present a mapping algorithm to compute large-scale magnetic field maps in indoor environments. In our simulations, we show that our method achieves better accuracy than current state-of-the-art methods on magnetic field maps with a growing mapping area.
  arXiv  Detail & Related papers  (2023-10-25T11:58:18Z)
• Linearized Wasserstein dimensionality reduction with approximation guarantees [65.16758672591365]
  LOT Wassmap is a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space. We show that LOT Wassmap attains correct embeddings and that the quality improves with increased sample size. We also show how LOT Wassmap significantly reduces the computational cost when compared to algorithms that depend on pairwise distance computations.
  arXiv  Detail & Related papers  (2023-02-14T22:12:16Z)
• Gaussian process regression and conditional Karhunen-Lo\'{e}ve models for data assimilation in inverse problems [68.8204255655161]
  We present a model inversion algorithm, CKLEMAP, for data assimilation and parameter estimation in partial differential equation models. The CKLEMAP method provides better scalability compared to the standard MAP method.
  arXiv  Detail & Related papers  (2023-01-26T18:14:12Z)
• Indoor SLAM Using a Foot-mounted IMU and the local Magnetic Field [1.9981375888949475]
  The algorithm uses two maps, namely, a motion map and a magnetic field map. The motion map captures typical motion patterns of pedestrians in buildings constrained by corridors and doors. The results show the efficacy of the algorithm in localizing pedestrians in indoor environments.
  arXiv  Detail & Related papers  (2022-03-29T19:18:02Z)
• A Metaheuristic Algorithm for Large Maximum Weight Independent Set Problems [58.348679046591265]
  Given a node-weighted graph, find a set of independent (mutually nonadjacent) nodes whose node-weight sum is maximum. Some of the graphs airsing in this application are large, having hundreds of thousands of nodes and hundreds of millions of edges. We develop a new local search algorithm, which is a metaheuristic in the greedy randomized adaptive search framework.
  arXiv  Detail & Related papers  (2022-03-28T21:34:16Z)
• A Domain-Shrinking based Bayesian Optimization Algorithm with Order-Optimal Regret Performance [16.0251555430107]
  This is the first GP-based algorithm with an order-optimal regret guarantee. Compared with the prevailing GP-UCB family of algorithms, the proposed algorithm reduces computational complexity by a factor of $O(T2d-1)$.
  arXiv  Detail & Related papers  (2020-10-27T02:15:15Z)
• Local optimization on pure Gaussian state manifolds [63.76263875368856]
  We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm. The method is based on notions of descent gradient attuned to the local geometry. We use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.
  arXiv  Detail & Related papers  (2020-09-24T18:00:36Z)
• Making Affine Correspondences Work in Camera Geometry Computation [62.7633180470428]
  Local features provide region-to-region rather than point-to-point correspondences. We propose guidelines for effective use of region-to-region matches in the course of a full model estimation pipeline. Experiments show that affine solvers can achieve accuracy comparable to point-based solvers at faster run-times.
  arXiv  Detail & Related papers  (2020-07-20T12:07:48Z)
• Accelerated Message Passing for Entropy-Regularized MAP Inference [89.15658822319928]
  Maximum a posteriori (MAP) inference in discrete-valued random fields is a fundamental problem in machine learning. Due to the difficulty of this problem, linear programming (LP) relaxations are commonly used to derive specialized message passing algorithms. We present randomized methods for accelerating these algorithms by leveraging techniques that underlie classical accelerated gradient.
  arXiv  Detail & Related papers  (2020-07-01T18:43:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.