We investigate which higher rank simple Lie groups admit profinitely but not abstractly commensurable lattices. We show that no such examples exist for the complex forms of type $E_8$, $F_4$, and $G_2$. In contrast, there are arbitrarily many such examples in all other higher rank Lie groups, except possibly $\textrm{SL}_{2n+1}(\mathbb{R})$, $\textrm{SL}_{2n+1}(\mathbb{C})$, $\textrm{SL}_n(\mathbb{H})$, or groups of type $E_6$.

A new method is proposed for determining a ship's position at sea using naturally occurring pulsar signals to provide an alternative to the sextant. Use is made of four distinct pulsar radio signals whose timing stabilities are comparable to atomic clocks and whose characteristic signatures can be used as natural radio navigation beacons. Pulse peak time difference measurements, accurate to within 10−5 and 10−6 s, were generated for a key reference observatory which provides long-term pulsar timing observations and for the unknown ship location. These time differences when multiplied by the velocity of light provide a distance value that is fundamental in calculating the ship's position. Resultant simulations provided a position accuracy to ≈1⋅1 km (≈0⋅6 nm) for the higher timing difference measurement. A single-pulsar-based approach, which gave a position accuracy to ≈2⋅8 km (≈1⋅5 nm), was also investigated for affordable equipment solutions and comparison with NASA space-based navigation experiments.

In this paper, we propose a sea current relative navigation method using an interacting multiple model (IMM) filter with adaptive fading technique that can compensate an inaccurate sea current dynamics model. Due to the marine environment, the underwater vehicles largely depend on inertial navigation. Unfortunately, since its performance deteriorates with time, it is usually aided by another sensor. An electromagnetic-log (EM-log) and a Doppler velocity log (DVL), which are mainly used in marine navigation, provide relative velocity measurements to the sea currents, and hence require an accurate sea current dynamics model to fully utilise them. However, it is difficult to reflect the actual sea current changes with just a single fixed model, resulting in degraded overall navigation performance. Therefore, this paper proposes an IMM filter that can use multiple sea current dynamics models and has sub-filters designed with adaptive fading extended Kalman filter (AFEKF) to compensate for the mismodelling of sea current dynamics. The method is verified by simulation and shows a performance improvement comparable to the optimal filter.

Because of the high photon flux, the Crab nebula pulsar is widely used as the observation target for X-ray pulsar-based navigation. The built profile of the Crab pulsar will change over time, however, which means that the pre-calibrated template cannot be used for the long term. In this paper, a novel pulsar-based template-independent navigation method is proposed. The detected phase propagation model is given as a term of position of the vehicle, taking the orbital motion into account. A different method of time-of-arrival process between the recovered profiles is introduced. With the aid of orbital transition matrix, a measurement model is derived to be a term of velocity error of the vehicle varying with time. The state errors of the vehicle are transformed into velocity errors by performing multi-segment observations to achieve the navigation system observability. The navigation equations of the system are then established and can be solved directly. Some simulations are performed to verify the method and suggest that the proposed method is feasible, effective and easy to implement. The precise orbit information of the vehicle can be determined. The state estimation accuracy is basically consistent with the traditional filtering algorithms, and the computational cost is still very low.

To verify whether a graph is suitable for describing driver behaviour performance under the effects of navigation information, this study applies two types of prompt messages: simple and detailed. The simple messages contain only direction instructions, while the detailed messages contain distance, direction, road and lane instructions. A driving simulation experiment was designed to collect the empirical data. Two vehicle operating indicators (velocity and lateral offset), and two driver manoeuvre indicators (accelerator power and steering wheel angle) were selected, and T-test was used to compare the differences of behavioural performance. Driving behaviour graphs were constructed for the two message conditions; their characteristics and similarities were further analysed. Finally, the results of T-test of behavioural performance and similarity results of the driving behaviour graphs were compared. Results indicated that the two different types of prompt messages were associated with significant differences in driving behaviours, which implies that it is feasible to describe the characteristics of driving behaviours guided by navigation information using such graphs. This study provides a new method for systematically exploring the mechanisms affecting drivers’ response to navigation information, and presents a new perspective for the optimisation of navigation information.

This study summarises the scenario of maritime traffic anomalies, like the increased congestion and U-turn of ships caused by the ship grounding in the Suez Canal in March 2021. Here, satellite automatic identification system based ship trajectories, and Sentinel-1 and Sentinel-2 images based ship positions are analysed after subdividing the study area into seas, lakes and canals. The results show that the blockage affected the maritime traffic for more than three weeks, waiting ship numbers increased from 5 to 122, and daily one to three ships made a U-turn between 23 and 31 March in the Gulf of Suez. Ship density also increased to more than double in Bitter Lakes with a minimum waiting time of 7 days. Hence, to avoid such prolonged waiting of ships, we propose a warning method based on the sharp speed decrease rate, U-turn and congestion.