Sub-Resolution mmWave FMCW Radar-based Touch Localization using Deep Learning

Touchscreen-based interaction on display devices are ubiquitous nowadays. However, capacitive touch screens, the core technology that enables its widespread use, are prohibitively expensive to be used in large displays because the cost increases proportionally with the screen area. In this paper, we propose a millimeter wave (mmWave) radar-based solution to achieve subresolution error performance using a network of four mmWave radar sensors. Unfortunately, achieving this is non-trivial due to inherent range resolution limitations of mmWave radars, since the target (human hand, finger etc.) is 'distributed' in space. We overcome this using a deep learning-based approach, wherein we train a deep convolutional neural network (CNN) on range-FFT (range vs power profile)-based features against ground truth (GT) positions obtained using a capacitive touch screen. To emulate the clutter characteristics encountered in radar-based positioning of human fingers, we use a metallic finger mounted on a metallic robot arm as the target. Using this setup, we demonstrate subresolution position error performance. Compared to conventional signal processing (CSP)-based approaches, we achieve a 2-3x reduction in positioning error using the CNN. Furthermore, we observe that the inference time performance and CNN model size support real-time integration of our approach on general purpose processor-based computing platforms.

Iterative RNDOP-Optimal Anchor Placement for Beyond Convex Hull ToA-based Localization: Performance Bounds and Heuristic Algorithms

Localizing targets outside the anchors' convex hull is an understudied but prevalent scenario in vehicle-centric, UAV-based, and self-localization applications. Considering such scenarios, this paper studies the optimal anchor placement problem for Time-of-Arrival (ToA)-based localization schemes such that the worst-case Dilution of Precision (DOP) is minimized. Building on prior results on DOP scaling laws for beyond convex hull ToA-based localization, we propose a novel metric termed the Range-Normalized DOP (RNDOP). We show that the worst-case DOP-optimal anchor placement problem simplifies to a min-max RNDOP-optimal anchor placement problem. Unfortunately, this formulation results in a non-convex and intractable problem under realistic constraints. To overcome this, we propose iterative anchor addition schemes, which result in a tractable albeit non-convex problem. By exploiting the structure arising from the resultant rank-1 update, we devise three heuristic schemes with varying performance-complexity tradeoffs. In addition, we also derive the upper and lower bounds for scenarios where we are placing anchors to optimize the worst-case (a) 3D positioning error and (b) 2D positioning error. We build on these results to design a cohesive iterative algorithmic framework for robust anchor placement and then discuss the computational complexity of the proposed schemes. Using numerical results, we validate the accuracy of our theoretical results. We also present comprehensive Monte-Carlo simulation results to compare the positioning error and execution time performance of each iterative scheme, discuss the tradeoffs, and provide valuable system design insights for beyond convex hull localization scenarios.