Series Expansion Approximations of Brownian Motion for Non-Linear Kalman Filtering of Diffusion Processes

In this paper, we describe a novel application of sigma-point methods to continuous-discrete filtering. In principle, the nonlinear continuous- discrete filtering problem can be solved exactly. In practice, the solution contains terms that are computationally intractible. Assumed density filtering methods attempt to match statistics of the filtering distribution to some set of more tractible probability distributions. We describe a novel method that decomposes the Brownian motion driving the signal in a generalised Fourier series, which is truncated after a number of terms. This approximation to Brownian can be described using a relatively small number of Fourier coefficients, and allows us to compute statistics of the filtering distribution with a single application of a sigma-point method. Assumed density filters that exist in the literature usually rely on discretisation of the signal dynamics followed by iterated application of a sigma point transform (or a limiting case thereof). Iterating the transform in this manner can lead to loss of information about the filtering distri- bution in highly nonlinear settings. We demonstrate that our method is better equipped to cope with such problems

Robot Mapping and Localisation for Feature Sparse Water Pipes Using Voids as Landmarks

Robotic systems for water pipe inspection do not generally include navigation components for mapping the pipe network and locating damage. Such navigation systems would be highly advantageous for water companies because it would allow them to more effectively target maintenance and reduce costs. In water pipes, a major challenge for robot navigation is feature sparsity. In order to address this problem, a novel approach for robot navigation in water pipes is developed here, which uses a new type of landmark feature - voids outside the pipe wall, sensed by ultrasonic scanning. The method was successfully demonstrated in a laboratory environment and showed for the first time the potential of using voids for robot navigation in water pipes

Posterior Linearization Filter: Principles and Implementation Using Sigma Points

This paper is concerned with Gaussian approximations to the posterior probability density function (PDF) in the update step of Bayesian filtering with nonlinear measurements. In this setting, sigma-point approximations to the Kalman filter (KF) recursion are widely used due to their ease of implementation and relatively good performance. In the update step, these sigma-point KFs are equivalent to linearizing the nonlinear measurement function by statistical linear regression (SLR) with respect to the prior PDF. In this paper, we argue that the measurement function should be linearized using SLR with respect to the posterior rather than the prior to take into account the information provided by the measurement. The resulting filter is referred to as the posterior linearization filter (PLF). In practice, the exact PLF update is intractable but can be approximated by the iterated PLF (IPLF), which carries out iterated SLRs with respect to the best available approximation to the posterior. The IPLF can be seen as an approximate recursive Kullback-Leibler divergence minimization procedure. We demonstrate the high performance of the IPLF in relation to other Gaussian filters in two numerical examples

Automatic Sleep Arousal Detection Using State Distance Analysis in Phase Space

Defective sleep arousal can contribute to significant sleep-related injuries and affect the quality of life. Investigating the arousal process is a challenging task as most of such events may be associated with subtle electrophysiological indications. Thus, developing an accurate model is an essential step toward the diagnosis and assessment of arousals. Here we introduce a novel approach for automatic arousal detection inspired by the states' recurrences in nonlinear dynamics. We first show how the states distance matrices of a complex system can be reconstructed to decrease the effect of false neighbors. Then, we use a convolutional neural network for probing the correlated structures inside the distance matrices with the arousal occurrences. Contrary to earlier studies in the literature, the proposed approach focuses on the dynamic behavior of polysomnography recordings rather than frequency analysis. The proposed approach is evaluated on the training dataset in a 3-fold cross-validation scheme and achieved an average of 19.20% and 78.57% for the area under the precision-recall (AUPRC) and area under the ROC curves, respectively. The overall AUPRC on the unseen test dataset is 19%. ? 2018 Creative Commons Attribution

Sensors and AI Techniques for Situational Awareness in Autonomous Ships: A Review

Autonomous ships are expected to improve the level of safety and efficiency in future maritime navigation. Such vessels need perception for two purposes: to perform autonomous situational awareness and to monitor the integrity of the sensor system itself. In order to meet these needs, the perception system must fuse data from novel and traditional perception sensors using Artificial Intelligence (AI) techniques. This article overviews the recognized operational requirements that are imposed on regular and autonomous seafaring vessels, and then proceeds to consider suitable sensors and relevant AI techniques for an operational sensor system. The integration of four sensors families is considered: sensors for precise absolute positioning (Global Navigation Satellite System (GNSS) receivers and Inertial Measurement Unit (IMU)), visual sensors (monocular and stereo cameras), audio sensors (microphones), and sensors for remote-sensing (RADAR and LiDAR). Additionally, sources of auxiliary data, such as Automatic Identification System (AIS) and external data archives are discussed. The perception tasks are related to well-defined problems, such as situational abnormality detection, vessel classification, and localization, that are solvable using AI techniques. Machine learning methods, such as deep learning and Gaussian processes, are identified to be especially relevant for these problems. The different sensors and AI techniques are characterized keeping in view the operational requirements, and some example state-of-the-art options are compared based on accuracy, complexity, required resources, compatibility and adaptability to maritime environment, and especially towards practical realization of autonomous systems