This paper presents a robust train localisation system by fusing a Global Navigation Satellite System (GNSS) with an Inertial Navigation System (INS) in a tightly-coupled (TC) strategy. To improve navigation performance in GNSS partly blocked areas, an advanced map-matching (MM) measurement-augmented TC GNSS/INS method is proposed via an error-state unscented Kalman filter (UKF). The advanced MM generates a matched position using a one-step predicted position from a UKF time update step with binary search algorithm and a point–line projection algorithm. The matched position inputs as an additional measurement to fuse with the INS position to augment the degraded GNSS pseudorange measurement to optimise the state estimation in the UKF measurement update step. Both the real train test on the Qinghai–Tibet railway and the simulation were carried out and the results confirm that the proposed advanced MM measurement-augmented TC GNSS/INS with error-state UKF provides the best horizontal positioning accuracy of 0 ⋅ 67 m, which performs an improvement of about 71% and 90% with respect to TC GNSS/INS with only error-state UKF and only error-state Extended Kalman filter in GNSS partly blocked areas.

Electronic navigational charts (ENCs) can be compiled using existing paper charts to improve their coverage of the world's oceans. However, in the process of assigning symbols on ENCs, in some cases the software uses the same symbol for different paper chart symbols. This could ultimately compromise maritime safety. Addressing this issue, this paper describes a methodology for developing a new tool that complements the efficient production of ENCs using paper charts. First, the ENC product was produced utilising CARIS S-57 Composer. After considering the difficulties in assigning symbols through the compilation process, a new web application named SYMO EXPERT was introduced. It was developed using Firebase Realtime Database and React app. A questionnaire was prepared to collect data about the time factor and accuracy of using SYMO EXPERT. Results showed that it supports the users in selecting relevant symbols efficiently with an accuracy of up to 98%.

Due to the exceptional complexity of the propulsion system (sails), square-riggers form a special group of sailing vessels. In modern pleasure and sport sailing, simple Bermuda (triangular) sailing rigging prevails, which is widely discussed in the literature, both in terms of theory and numerous experiments. The literature on the theory on square-riggers is, in turn, limited mainly to the description of good sailing practice developed over the centuries. Its important element was maximising vessel speed, but this discussion has not been documented by scientific research. This paper presents the significant parameters influencing the speed of a square-rigged sailing vessel and selects those which are the most important from the point of view of its maximisation. The paper also proposes methods and measurement systems which optimise selected parameters affecting the achievement of higher speeds. The paper describes the types of speeds of typical sailing vessels, provides a historical synthesis of sailing ships with respect to their speed, and presents a selection and description of the parameters affecting the speed of modern square-rigged vessels. The paper ends with a proposed method and measurement system for experimental research aiming at rigging optimisation in a square-rigged sailing vessel from the point of view of maximising its speed.

As no internationally agreed-upon method for determining safe speed values currently exists, collecting vast amounts of information on conventional ship behaviour could be used to train autonomous ship intelligence in determining safe speeds in different conditions. This requires speed data collected from conventional ships to resemble what can be described as safe speeds. To test this, the Automatic Identification System (AIS) and environmental data – namely visibility, mean wind speed and significant wave height – were collected and merged for two study areas in Norway in the period between 27 March 2014 and 1 January 2021. Regression analyses based on 47,490 unique vessel transits were conducted and supplemented by two graphical methods for revealing relationships between variables. Contrary to the contemporary understanding of safe speed, reduced visibility did not lead to significantly reduced transit speeds. Wind and waves caused a reduction in speed in the open ocean, but not in coastal waters. Transit speeds were lower in coastal waters than in the open ocean.

Concentrating on a surface vessel with input saturation, model uncertainties and unknown disturbances, a path following the adaptive backstepping control method based on prescribed performance line-of-sight (PPLOS) guidance is proposed. First, a prescribed performance asymmetric modified barrier Lyapunov function (PPAMBLF) is used to design the PPLOS and the heading controller, which make the path following position and heading errors meet the prescribed performance requirements. Furthermore, the backstepping and dynamic surface technique (DSC) are used to design the path following controller and the adaptive assistant systems are constructed to compensate the influence of input saturation. In addition, neural networks are introduced to approximate model uncertainties, and the adaptive laws are designed to estimate the bounds of the neural network approximation errors and unknown disturbances. According to the Lyapunov stability theory, all signals are semi-globally uniformly ultimately bounded. Finally, a 76$\,{\cdot }\,$2 m supply surface vessel is used for simulation experiments. The experimental results show that although the control inputs are limited, the control system can still converge quickly, and both position and heading errors can be limited to the prescribed performance requirements.

The use of the required navigation performance (RNP) procedure has been increasing for aircraft navigation, since it allows for better optimisation of the airspace, which is increasingly congested. The present work aims to investigate the application of the functional resonance analysis method (FRAM), combined with the quantitative analysis provided by the Bayesian belief network (BBN), to demonstrate the existing variability in functions that are part of the complex navigation system based on the RNP procedure, specifically when the aircraft approaches the airport (approach phase). As a result, it is possible to analyse the variability that occurs in the studied system and the BBN complemented the study by allowing a quantitative interpretation of the functions considered most important for the execution of an RNP approach procedure.

The algebraic K-theory of Lawvere theories is a conceptual device to elucidate the stable homology of the symmetry groups of algebraic structures such as the permutation groups and the automorphism groups of free groups. In this paper, we fully address the question of how Morita equivalence classes of Lawvere theories interact with algebraic K-theory. On the one hand, we show that the higher algebraic K-theory is invariant under passage to matrix theories. On the other hand, we show that the higher algebraic K-theory is not fully Morita invariant because of the behavior of idempotents in non-additive contexts: We compute the K-theory of all Lawvere theories Morita equivalent to the theory of Boolean algebras.

We address Hodge integrals over the hyperelliptic locus. Recently Afandi computed, via localisation techniques, such one-descendant integrals and showed that they are Stirling numbers. We give another proof of the same statement by a very short argument, exploiting Chern classes of spin structures and relations arising from Topological Recursion in the sense of Eynard and Orantin.

These techniques seem also suitable to deal with three orthogonal generalisations: (1) the extension to the r-hyperelliptic locus; (2) the extension to an arbitrary number of non-Weierstrass pairs of points; (3) the extension to multiple descendants.

We prove that if K is a nontrivial null-homotopic knot in a closed oriented 3–manfiold Y such that $Y-K$ does not have an $S^1\times S^2$ summand, then the zero surgery on K does not have an $S^1\times S^2$ summand. This generalises a result of Hom and Lidman, who proved the case when Y is an irreducible rational homology sphere.