Automatic Identification System (AIS) provides estimated position time along with reception time and a time stamp at the receiving station; however, the exact position estimation time remains unidentified. Therefore, this study examines the extent of positional error when using current AIS reception time. As a result, a maximum positional error of 116.9 m was observed between AIS and RTK-GPS (Real-Time Kinematic GPS). Subsequent time correction reduced this error to less than 10 m, with the product of ship speed and correction time nearly matching the error pre-correction. Consequently, it was concluded that transmitting position estimation time is essential for maintaining the reliability of Position Accuracy transmitted by AIS or VHF Data Exchange System (VDES). Furthermore, VDES may possess the communication capacity to transmit and receive vessel attitude data. Therefore, to assess the required transmission frequency, the data transmission period of roll and pitch attitude data was analysed through the mutual correlation of acceleration and angular velocity. The results indicated that the correlation coefficient for each axis exceeded 0.65 at frequencies of 0.5 Hz or higher.

Global Navigation Satellite Systems (GNSS) positioning and integrity monitoring models and algorithms currently generically assume that measurement errors follow a Gaussian distribution. As this is not always the case, there is a trade-off affecting system safety and availability, emphasising the need for better error characterisation in mission-critical applications. Research to date has shown advantages of Generalised Extreme Value (GEV) distribution for mapping extreme events. However, it is more complex than the Gaussian distribution, especially in the error convolution process. This paper derives a distribution, referred to as the GEV-based Gaussian distribution, that benefits from the advantages of both the GEV and Gaussian distributions in mapping extreme events and simplicity, respectively. The proposed distribution is tested against Gaussian, GEV and Generalised t distribution. The results show that the proposed distribution can provide a better bound for extreme events than the tested distribution both for pseudorange and carrier phase errors.

In this paper, we investigate extensions between graded Verma modules in the Bernstein–Gelfand–Gelfand category $\mathcal{O}$. In particular, we determine exactly which information about extensions between graded Verma modules is given by the coefficients of the R-polynomials. We also give some upper bounds for the dimensions of graded extensions between Verma modules in terms of Kazhdan–Lusztig combinatorics. We completely determine all extensions between Verma module in the regular block of category $\mathcal{O}$ for $\mathfrak{sl}_4$ and construct various “unexpected” higher extensions between Verma modules.

We classify hyperbolic polynomials in two real variables that admit a transitive action on some component of their hyperbolic level sets. Such surfaces are called special homogeneous surfaces, and they are equipped with a natural Riemannian metric obtained by restricting the negative Hessian of their defining polynomial. Independent of the degree of the polynomials, there exist a finite number of special homogeneous surfaces. They are either flat, or have constant negative curvature.

Traditional radiometric tracking navigation increasingly fails to meet the demands of deep space exploration. In contrast, optical navigation enables interplanetary spacecraft to navigate autonomously with higher precision. The effectiveness of image processing algorithms plays a crucial role in determining the accuracy of optical navigation systems. This paper presents a robust centroid extraction method based on a hybrid genetic algorithm. First, noise interference is effectively reduced by leveraging proximity information. Second, a fitness evaluation mechanism is introduced to assess model performance throughout the iterative process. Third, an annealing mutation operator is incorporated to prevent premature convergence to local optima. Finally, extensive comparative testing demonstrates that the proposed method offers substantial improvements in both accuracy and robustness, thereby substantially improving the reliability of the navigation system under complex conditions.

The recently discovered social place cells and grid cells in hippocampal formation are believed to be the neural basis underlying relative navigation of conspecifics. In this paper, we propose a new brain-inspired relative navigation model in a large-scale 3D environment for collective UAVs that translates the neurodynamics of the social place cell–grid cell circuit to robotic relative navigation algorithm for the first time. Our approach comprises three key parts: (1) a 3D isotropic Gaussian function-based cube social place cell network (cube-SPCNet), (2) a 3D continuous attractor neural network-based cube grid cell network (cube-GCNet), and (3) a population vector-based neural decoding module. The resulting brain-inspired relative navigation model incorporates the good relative information abstraction capabilities of the cube-SPCNet with the powerful temporal filtering capabilities of the cube-GCNet, yielding robustness and accuracy performance improvement for relative navigation. Experimental results show the new method can provide more robust and precise relative navigation results than its conventional counterpart, displaying a possible brain-inspired solution for relative navigation enhancement for collective UAVs.

In this paper, we provide sufficient conditions for a space X to satisfy the Ganea conjecture for topological complexity. To achieve this, we employ two auxiliary invariants: weak topological complexity in the sense of Berstein–Hilton, along with a certain stable version of it. Several examples are discussed.

Among the artefacts recovered from Warwick, an English ship wrecked in Bermuda at the end of November 1619, was a small wooden navigational device. Discovered during the 2010 archaeological field season, the object was cleaned, analysed, and later conserved. It has been identified as an analogue navigational tool known as a plain scale. A novel instrument at the time, the device showed real-world applications of complex mathematical formulas for charting a course on a map. Its presence on Warwick is striking; it is believed to be the earliest known example of a plain scale in use on board an English ship sailing to the colonies. The goal of this paper is to present the artefact, provide its historical and archaeological background, and discuss the current body of research related to its purpose in resolving navigational problems.

We show that for an oriented 4-dimensional Poincaré complex X with finite fundamental group, whose 2-Sylow subgroup is abelian with at most 2 generators, the homotopy type of X is determined by its quadratic 2-type.

Three-dimensional mapping-aided (3DMA) Global Navigation Satellite System (GNSS) positioning improves the positioning in urban canyons for non-precision GNSS receivers. However, the 3DMA GNSS algorithms often produce a multimodal position solution, and simply taking the average of these modes reduces accuracy. A further problem, named ‘solution shifting’, is the effect of large numbers of low-scoring candidates shifting the overall position solution away from high-scoring regions. This study uses a clustering method to separate the different modes and exclude low-scoring regions from the position solution. Factor graph optimisation (FGO) is then used to integrate clustered 3DMA GNSS position and GNSS Doppler measurements or estimated velocity over multiple epochs. Positioning performance is assessed using data collected in London. The results show that the clustering method can successfully mitigate the multimodal effect, and integrating the FGO can mitigate the occurrence of multimodality and solution shifting. Static experiments in London achieve an RMSE of approximately 10 m for FGO 3DMA GNSS with clustering and 11 m without clustering.

Aviation employees operate in a dynamic, complex safety-critical system that is filled with uncertainty, requiring quick and correct expert decision-making. The purpose of this study is to investigate the decision-making indicators among aviation employees. Fifty-five technical engineers and air traffic controllers participated in this study by completing the Cambridge Gambling Task (CGT) at one of Iran’s airports. The CGT provides one of the most reliable and widely used decision-making assessment tasks and related indicators, including decision-making quality, risk-taking, delay aversion, deliberation time, risk adjustment and overall bet ratio. Higher risk adjustment, less deliberation time, and a lower delay aversion index resulted in better decision-making quality. Higher risk-taking does not necessarily mean lower self-control. No significant differences were observed between the studied groups, including between air traffic controllers (both Ground and Tower vs. RADAR and Approach) and between air traffic controllers and technical engineers in the CGT performance. The decision-making quality increased with age and work experience, which has important implications for training and selection processes.

A long standing conjecture states that the ropelength of any alternating knot is at least proportional to its crossing number. In this paper we prove that this conjecture is true. That is, there exists a constant $b_0 \gt 0$ such that $R(K)\ge b_0Cr(K)$ for any alternating knot K, where R(K) is the ropelength of K and Cr(K) is the crossing number of K. In this paper, we prove that this conjecture is true and establish that $b_0 \gt 1/56$.

We investigate the joint distribution of L-functions on the line $ \sigma= {1}/{2} + {1}/{G(T)}$ and $ t \in [ T, 2T]$, where $ \log \log T \leq G(T) \leq { \log T}/{ ( \log \log T)^2 } $. We obtain an upper bound on the discrepancy between the joint distribution of L-functions and that of their random models. As an application we prove an asymptotic expansion of a multi-dimensional version of Selberg’s central limit theorem for L-functions on $ \sigma= 1/2 + 1/{G(T)}$ and $ t \in [ T, 2T]$, where $ ( \log T)^\varepsilon \leq G(T) \leq { \log T}/{ ( \log \log T)^{2+\varepsilon } } $ for $ \varepsilon > 0$.

The complex tasks of air traffic control (ATC) and the various factors affecting its operation have shed light on the need to build a model to predict conflict detection and resolution (CDR) performance within a traffic situation. This study aimed at developing a fuzzy-hybrid framework for quantifying various aspects in ATC consisting of the software, hardware, environment, liveware and organisation (i.e. the SHELL model) to predict CDR performance. The proposed fuzzy-hybrid SHELL framework in this study was tested using metadata from 10 prior studies in ATC. The results showed a highly accurate prediction, as indicated by the RMSE and MAPE values of 0⋅09 and 5⋅36%, respectively, indicating a high consistency of 90⋅92% for predicting the CDR performance. This framework offers a promising approach for Air Navigation Service Providers (ANSPs) to maintain air traffic safety and improve ATC operations efficiency.

In this note we investigate the centraliser of a linearly growing element of $\mathrm{Out}(F_n)$ (that is, a root of a Dehn twist automorphism), and show that it has a finite index subgroup mapping onto a direct product of certain “equivariant McCool groups” with kernel a finitely generated free abelian group. In particular, this allows us to show it is VF and hence finitely presented.

The Singapore Strait, as one of the busiest shipping waterways in the world, contains two chokepoints of the Straits of Malacca and Singapore. With an increasing number of large-sized ships passing through the Singapore Strait in recent years, its traffic capacity has undoubtedly been affected significantly. Therefore, this study aims to assess the traffic capacity of the Singapore Strait under various mixed vessel compositions including different vessel types, vessel sizes and traffic volumes. A ship domain-based method for the estimation of the strait capacity and its variance is derived by using the minimum distance to collision among various vessel types. Then, based on the Automatic Identification System data, the strait capacity and its variances are quantitatively estimated for the two chokepoints of this waterway. Our results confirm that the strait capacity is decreasing with an increasing proportion of large-sized ships. It is also found that this traffic capacity is directly affected by the width of the strait, the size, the composition and the speed of the ships.

For $g \geqslant 2$, we show that the number of positive integers at most X which can be written as sum of two base g palindromes is at most ${X}/{\log^c X}$. This answers a question of Baxter, Cilleruelo and Luca.