Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. Compared to classical numerical methods, PINNs have several advantages, for example their ability to provide mesh-free solutions of differential equations and their ability to carry out forward and inverse modelling within the same optimisation problem. Whilst promising, a key limitation to date is that PINNs have struggled to accurately and efficiently solve problems with large domains and/or multi-scale solutions, which is crucial for their real-world application. Multiple significant and related factors contribute to this issue, including the increasing complexity of the underlying PINN optimisation problem as the problem size grows and the spectral bias of neural networks. In this work, we propose a new, scalable approach for solving large problems relating to differential equations called finite basis physics-informed neural networks (FBPINNs). FBPINNs are inspired by classical finite element methods, where the solution of the differential equation is expressed as the sum of a finite set of basis functions with compact support. In FBPINNs, neural networks are used to learn these basis functions, which are defined over small, overlapping subdomains. FBINNs are designed to address the spectral bias of neural networks by using separate input normalisation over each subdomain and reduce the complexity of the underlying optimisation problem by using many smaller neural networks in a parallel divide-and-conquer approach. Our numerical experiments show that FBPINNs are effective in solving both small and larger, multi-scale problems, outperforming standard PINNs in both accuracy and computational resources required, potentially paving the way to the application of PINNs on large, real-world problems.

In the last few decades, Structure from Motion (SfM) and visual Simultaneous Localization and Mapping (visual SLAM) techniques have gained significant interest from both the computer vision and robotic communities. Many variants of these techniques have started to make an impact in a wide range of applications, including robot navigation and augmented reality. However, despite some remarkable results in these areas, most SfM and visual SLAM techniques operate based on the assumption that the observed environment is static. However, when faced with moving objects, overall system accuracy can be jeopardized. In this article, we present for the first time a survey of visual SLAM and SfM techniques that are targeted toward operation in dynamic environments. We identify three main problems: how to perform reconstruction (robust visual SLAM), how to segment and track dynamic objects, and how to achieve joint motion segmentation and reconstruction. Based on this categorization, we provide a comprehensive taxonomy of existing approaches. Finally, the advantages and disadvantages of each solution class are critically discussed from the perspective of practicality and robustness.

Extracting robust and general 3D local features is key to downstream tasks such as point cloud registration and reconstruction. Existing learning-based local descriptors are either sensitive to rotation transformations, or rely on classical handcrafted features which are neither general nor representative. In this paper, we introduce a new, yet conceptually simple, neural architecture, termed SpinNet, to extract local features which are rotationally invariant whilst sufficiently informative to enable accurate registration. A Spatial Point Transformer is first introduced to map the input local surface into a carefully designed cylindrical space, enabling end-to-end optimization with SO(2) equivariant representation. A Neural Feature Extractor which leverages the powerful point-based and 3D cylindrical convolutional neural layers is then utilized to derive a compact and representative descriptor for matching. Extensive experiments on both indoor and outdoor datasets demonstrate that SpinNet outperforms existing state-of-the-art techniques by a large margin. More critically, it has the best generalization ability across unseen scenarios with different sensor modalities. The code is available at https://github.com/QingyongHu/SpinNet.

Inertial sensors play a pivotal role in indoor localization, which in turn lays the foundation for pervasive personal applications. However, low-cost inertial sensors, as commonly found in smartphones, are plagued by bias and noise, which leads to unbounded growth in error when accelerations are double integrated to obtain displacement. Small errors in state estimation propagate to make odometry virtually unusable in a matter of seconds. We propose to break the cycle of continuous integration, and instead segment inertial data into independent windows. The challenge becomes estimating the latent states of each window, such as velocity and orientation, as these are not directly observable from sensor data. We demonstrate how to formulate this as an optimization problem, and show how deep recurrent neural networks can yield highly accurate trajectories, outperforming state-of-the-art shallow techniques, on a wide range of tests and attachments. In particular, we demonstrate that IONet can generalize to estimate odometry for non-periodic motion, such as a shopping trolley or baby-stroller, an extremely challenging task for existing techniques.

Indoor wireless systems often operate under non-line-of-sight (NLOS) conditions that can cause ranging errors for location-based applications. As such, these applications could benefit greatly from NLOS identification and mitigation techniques. These techniques have been primarily investigated for ultra-wide band (UWB) systems, but little attention has been paid to WiFi systems, which are far more prevalent in practice. In this study, we address the NLOS identification and mitigation problems using multiple received signal strength (RSS) measurements from WiFi signals. Key to our approach is exploiting several statistical features of the RSS time series, which are shown to be particularly effective. We develop and compare two algorithms based on machine learning and a third based on hypothesis testing to separate LOS/NLOS measurements. Extensive experiments in various indoor environments show that our techniques can distinguish between LOS/NLOS conditions with an accuracy of around 95%. Furthermore, the presented techniques improve distance estimation accuracy by 60% as compared to state-of-the-art NLOS mitigation techniques. Finally, improvements in distance estimation accuracy of 50% are achieved even without environment-specific training data, demonstrating the practicality of our approach to real world implementations.

The key to offering personalised services in smart spaces is knowing where a particular person is with a high degree of accuracy. Visual tracking is one such solution, but concerns arise around the potential leakage of raw video information and many people are not comfortable accepting cameras in their homes or workplaces. We propose a human tracking and identification system (mID) based on millimeter wave radar which has a high tracking accuracy, without being visually compromising. Unlike competing techniques based on WiFi Channel State Information (CSI), it is capable of tracking and identifying multiple people simultaneously. Using a lowcost, commercial, off-the-shelf radar, we first obtain sparse point clouds and form temporally associated trajectories. With the aid of a deep recurrent network, we identify individual users. We evaluate and demonstrate our system across a variety of scenarios, showing median position errors of 0.16 m and identification accuracy of 89% for 12 people.