Drift-Free Indoor Navigation Using Simultaneous Localization and Mapping of the Ambient Heterogeneous Magnetic Field

In the absence of external reference position information (e.g. GNSS) SLAM has proven to be an effective method for indoor navigation. The positioning drift can be reduced with regular loop-closures and global relaxation as the backend, thus achieving a good balance between exploration and exploitation. Although vision-based systems like laser scanners are typically deployed for SLAM, these sensors are heavy, energy inefficient, and expensive, making them unattractive for wearables or smartphone applications. However, the concept of SLAM can be extended to non-optical systems such as magnetometers. Instead of matching features such as walls and furniture using some variation of the ICP algorithm, the local magnetic field can be matched to provide loop-closure and global trajectory updates in a Gaussian Process (GP) SLAM framework. With a MEMS-based inertial measurement unit providing a continuous trajectory, and the matching of locally distinct magnetic field maps, experimental results in this paper show that a drift-free navigation solution in an indoor environment with millimetre-level accuracy can be achieved. The GP-SLAM approach presented can be formulated as a maximum a posteriori estimation problem and it can naturally perform loop-detection, feature-to-feature distance minimization, global trajectory optimization, and magnetic field map estimation simultaneously. Spatially continuous features (i.e. smooth magnetic field signatures) are used instead of discrete feature correspondences (e.g. point-to-point) as in conventional vision-based SLAM. These position updates from the ambient magnetic field also provide enough information for calibrating the accelerometer and gyroscope bias in-use. The only restriction for this method is the need for magnetic disturbances (which is typically not an issue indoors); however, no assumptions are required for the general motion of the sensor.Comment: ISPRS Workshop Indoor 3D 201

Identifying Sources and Sinks in the Presence of Multiple Agents with Gaussian Process Vector Calculus

In systems of multiple agents, identifying the cause of observed agent dynamics is challenging. Often, these agents operate in diverse, non-stationary environments, where models rely on hand-crafted environment-specific features to infer influential regions in the system's surroundings. To overcome the limitations of these inflexible models, we present GP-LAPLACE, a technique for locating sources and sinks from trajectories in time-varying fields. Using Gaussian processes, we jointly infer a spatio-temporal vector field, as well as canonical vector calculus operations on that field. Notably, we do this from only agent trajectories without requiring knowledge of the environment, and also obtain a metric for denoting the significance of inferred causal features in the environment by exploiting our probabilistic method. To evaluate our approach, we apply it to both synthetic and real-world GPS data, demonstrating the applicability of our technique in the presence of multiple agents, as well as its superiority over existing methods.Comment: KDD '18 Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Pages 1254-1262, 9 pages, 5 figures, conference submission, University of Oxford. arXiv admin note: text overlap with arXiv:1709.0235

Learning unknown ODE models with Gaussian processes

In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the underlying dynamics. In these settings, parametric ODE model cannot be formulated. Here, we overcome this issue by introducing a novel paradigm of nonparametric ODE modelling that can learn the underlying dynamics of arbitrary continuous-time systems without prior knowledge. We propose to learn non-linear, unknown differential functions from state observations using Gaussian process vector fields within the exact ODE formalism. We demonstrate the model's capabilities to infer dynamics from sparse data and to simulate the system forward into future.Comment: 11 pages, 2 page appendi

A spectrum of physics-informed Gaussian processes for regression in engineering

Despite the growing availability of sensing and data in general, we remain unable to fully characterize many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture human activity are unmatched in our engineered world, and, even in cases where data could be referred to as “big,” they will rarely hold information across operational windows or life spans. This paper pursues the combination of machine learning technology and physics-based reasoning to enhance our ability to make predictive models with limited data. By explicitly linking the physics-based view of stochastic processes with a data-based regression approach, a derivation path for a spectrum of possible Gaussian process models is introduced and used to highlight how and where different levels of expert knowledge of a system is likely best exploited. Each of the models highlighted in the spectrum have been explored in different ways across communities; novel examples in a structural assessment context here demonstrate how these approaches can significantly reduce reliance on expensive data collection. The increased interpretability of the models shown is another important consideration and benefit in this context