arXiv subjects

Muhammad Ammad

Publications and source records attributed to Muhammad Ammad.

6 recordsLinked to original sources

arXiv2026

Descriptor: A Hybrid Indoor and Indoor-Outdoor Positioning Multi-Technology Dataset (HYMN)

This article introduces the HYMN (HYbrid Multi-technology Navigation) dataset: a multi-system, and time synchronized dataset for localization research based on opportunistic signals collected in an indoor-outdoor scenario. HYMN comprises measurement data collected in an industrial hall setting for five different positioning systems including Ultra-Wideband (UWB), Bluetooth Low Energy (BLE), WiFi, 5G, and Global Navigation Satellite System (GNSS). Unlike existing datasets that focus on single technologies or purely indoor/outdoor scenarios, HYMN combines five positioning technologies with explicit coverage of indoor-outdoor transitions, enabling multi-sensor fusion research for seamless localization. Each instance of data is identified through a unique measurement id and it represents time-stamped observations relevant for each system respectively along with the ground truth information. HYMN is designed to support a wide range of localization tasks including multi-sensor fingerprinting, cross-technology fusion, and seamless indoor-outdoor positioning. The synchronized measurements from GNSS and other terrestrial systems enable researchers to investigate how heterogeneous signals complement each other to overcome individual technology limitations such as GNSS degradation in covered areas or terrestrial system variability in dynamic environments.

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arXiv2026

B-spline-Based ALE-MFS Framework for Evolving Domains

We develop and analyze a B-spline based arbitrary Lagrangian-Eulerian method of fundamental solutions (ALE-MFS) for curvature-driven motion of two-dimensional evolving domains. Boundary points move with the material to track the geometric flow, while interior points move within an ALE framework via a harmonic extension of the boundary velocity, computed by a meshless MFS with sources on a fixed auxiliary circle, thus avoiding volumetric meshing. Boundary normals and curvature are reconstructed by an adaptive local B-spline scheme that remains robust for strongly nonconvex shapes and large deformations. A posteriori error estimates are obtained from a hatmatrix formulation of leave-one-out cross-validation (LOOCV) for both square collocation and zero-padded least-squares systems, and are complemented by maximum principle indicators for harmonic problems. Numerical experiments on circular, star-shaped, and amoeba-like domains show that square collocation suffices for moderately complex geometries, while zero-padded least-squares significantly improves interior velocity regularity and pointwise transport accuracy for strongly nonconvex shapes, without altering the source or collocation sets. The ALE-MFS algorithm also generates high-quality moving meshes for ALE-finite element methods, with larger minimum angles and slower mesh ratio growth than classical FEM mesh-motion strategies, suggesting a practical and easily integrable alternative for challenging moving-interface simulations.

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arXiv2026

An Adaptive Lagrangian B-Spline Framework for Point Cloud Manifold Evolution

We extend our recent curve-evolution framework based on localized B-spline interpolation to present an adaptive Lagrangian framework for the geometric evolution of point-cloud data representing smooth, codimension-one surfaces in $\mathbb{R}^3$. The method constructs overlapping, localized tensor-product B-spline patches, enabling direct, meshless surface evolution from discrete samples. Within each patch, the differentiable B-spline representation yields analytic, high-order estimates of intrinsic geometric invariants, supporting curvature-driven and geometry-coupled flows. The organization of control points facilitates coherent updates of both surface samples and spline coefficients under intrinsic velocity fields. A conditioning-aware formulation of the local interpolation system, combined with a Gauss-Seidel refinement of control points, maintains interpolation quality throughout the evolution. Adaptive knot insertion and point redistribution, guided by geometric error indicators and local sampling density, preserve surface resolution and regularity during deformation. Numerical experiments demonstrate efficient and accurate reproduction of surface evolution phenomena, including mean-curvature flow, anisotropic deformations, and coupled surface-field dynamics, establishing localized B-spline methods as precise and versatile tools for dynamic manifold approximation.

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arXiv2026

Dirichlet Extremals for Discrete Plateau Problems in GT-Bezier Spaces via PSO

We study a discrete analogue of the parametric Plateau problem in a non-polynomial tensor-product surface spaces generated by the generalized trigonometric (GT)--B\'ezier basis. Boundary interpolation is imposed by prescribing the boundary rows and columns of the control net, while the interior control points are selected by a Dirichlet principle: for each admissible choice of B\'ezier basis shape parameters, we compute the unique Dirichlet-energy extremal within the corresponding GT--B\'ezier patch space, which yields a parameter-dependent symmetric linear system for the interior control net under standard nondegeneracy assumptions. The remaining design freedom is thereby reduced to a four-parameter optimization problem, which we solve by particle swarm optimization. Numerical experiments show that the resulting two-level procedure consistently decreases the Dirichlet energy and, in our tests, often reduces the realized surface area relative to classical Bernstein--B\'ezier Dirichlet patches and representative quasi-harmonic and bending-energy constructions under identical boundary control data. We further adapt the same Dirichlet-extremal methodology to a hybrid tensor-product/bilinear Coons framework, obtaining minimality-biased TB--Coons patches from sparse boundary specifications.

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arXiv2025

Efficient manifold evolution algorithm using adaptive B-Spline interpolation

This paper explores an efficient Lagrangian approach for evolving point cloud data on smooth manifolds. In this preliminary study, we focus on analyzing plane curves, and our ultimate goal is to provide an alternative to the conventional radial basis function (RBF) approach for manifolds in higher dimensions. In particular, we use the B-Spline as the basis function for all local interpolations. Just like RBF and other smooth basis functions, B-Splines enable the approximation of geometric features such as normal vectors and curvature. Once properly set up, the advantage of using B-Splines is that their coefficients carry geometric meanings. This allows the coefficients to be manipulated like points, facilitates rapid updates of the interpolant, and eliminates the need for frequent re-interpolation. Consequently, the removal and insertion of point cloud data become seamless processes, particularly advantageous in regions experiencing significant fluctuations in point density. The numerical results demonstrate the convergence of geometric quantities and the effectiveness of our approach. Finally, we show simulations of curvature flows whose speeds depend on the solutions of coupled reaction--diffusion systems for pattern formation.

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arXiv2025

Range-Angle Likelihood Maps for Indoor Positioning Using Deep Neural Networks

Accurate and high precision of the indoor positioning is as important as ensuring reliable navigation in outdoor environments. Using the state-of-the-art deep learning models provides better reliability and accuracy to navigate and monitor the accurate positions in the aircraft cabin environment. We utilize the simulated aircraft cabin environment measurements and propose a residual neural network (ResNet) model to predict the accurate positions inside the cabin. The measurements include the ranges and angles between a tag and the anchors points which are then mapped onto a grid as range and angle residuals. These residual maps are then transformed into the likelihood grid maps where each cell of the grid shows the likelihood of being a true location. These grid maps along with the true positions are then passed as inputs to train the ResNet model. Since any deep learning model involve numerous parameter settings, hyperparameter optimization is performed to get the optimal parameters for training the model effectively with the highest accuracy. Once we get the best hyperparameters settings of the model, it is then trained to predict the positions which provides a centimeter-level accuracy of the localization.

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