Whether Henry Ford or someone else gave us this famous quote, ‘If I had asked people what they wanted, they would have said faster horses’, we may agree that it implies there is a limit to what we can expect from the performance of an existing solution. Science and technology always try to push the boundaries and ‘improve’; improving the quality of our lives or improving the quality of technologies. We, as researchers in the area of navigation, are no exception; we want to improve the quality of navigation services. And there are many ways to do so, and challenges and limitations to those attempts. Some researchers look to improve the accuracy, the reliability, the integrity through different approaches. Some try to reduce or model noise, some try to minimise human error, and some use novel techniques and algorithms for better prediction. Of course, when ‘our horses cannot go any faster’ and there is not much space for improvement for a certain technology or service, researchers may come up with a completely new solution, such as an automobile. Almost all new technologies go through the same exploration period; at the beginning, we want to see how and if it works so we try simple tasks, but then we become more ambitious (or greedier!) and so we introduce it to more difficult challenges until it hits the breaking point. At this point, curious researchers and inventors try to push the boundaries and make the technology better, and if improvement is not possible, they build (invent) a new solution. But what is the ‘quality’ that many of us want to improve? How the quality of a technology or service can be measured in the first place?

In recent years, global navigation satellite system (GNSS) precise point positioning (PPP) has become a standard positioning technique for many applications with typically favourable open sky conditions, e.g. precision agriculture. Unfortunately, the long convergence (and reconvergence) time of PPP often significantly limits its use in difficult and restricted signal environments typically associated with urban areas. The modernisation of GNSS will positively affect and improve the convergence time of the PPP solutions, thanks to the higher number of satellites in view that broadcast multifrequency measurements. The number and geometry of the available satellites is a key factor that impacts on the convergence time in PPP, while triple-frequency observables have been shown to greatly benefit the fixing of the carrier phase integer ambiguities. On the other hand, many studies have shown that triple-frequency combinations do not usefully contribute to a reduction of the convergence time of float PPP solutions.

This paper proposes novel GPS and Galileo triple-carrier ionosphere-free combinations that aim to enhance the observability of the narrow-lane ambiguities. Tests based on simulated data have shown that these combinations can reduce the convergence time of the float PPP solution by a factor of up to 2·38 with respect to the two-frequency combinations. This approach becomes effective only after the extra wide-lane and wide-lane ambiguities have been fixed. For this reason, a new fixing method based on low-noise pseudo-range combinations corrected by the smoothed ionosphere correction is presented. By exploiting this algorithm, no more than a few minutes are required to fix the WL ambiguities for Galileo, even in cases of severe multipath environments.

Precise positioning with low-cost single-frequency global navigation satellite system (GNSS) receivers has great potential in a wide range of applications because of its low price and improved accuracy. However, challenges remain in achieving reliable and accurate solutions using low-cost receivers. For instance, the successful ambiguity fixing rate could be low for real-time kinematic (RTK) while large errors may occur in precise point positioning (PPP) in some scenarios (e.g., trees along the road). To solve the problems, this paper proposes a method with the aid of additional lane-level digital map information to improve the accuracy and reliability of RTK and PPP solutions. In the method, a digital camera will be applied for lane recognition and the positioning solution from a low-cost receiver will be projected to the digital map lane link. With the projected point position as a constraint, the RTK ambiguity fixing rate and PPP performance can be enhanced. A field kinematic test was conducted to verify the improvement of the RTK and PPP solutions with the aid of map matching. The results show that the RTK ambiguity fixing rate can be increased and the PPP positioning error can be reduced by map matching.

One critical issue in network real-time kinematic (NRTK) is the interpolation of atmospheric delay for user stations. Some classic interpolation algorithms, such as linear interpolation method (LIM), ignore the strong correlation between tropospheric delay and height factors, and the interpolation accuracy is poor in areas with large height difference. To solve this problem, a troposphere modelling method based on error compensation, namely ECDIM (Error Compensation-Based DIM), is proposed, and this method can be applied to both conventional single Delaunay triangulated network (DTN) and multi-station scenarios. The results of California Real Time Network (CRTN) with large height difference show that compared with LIM, the overall modelling accuracy with ECDIM has been improved by 50.1% to 67.3%, and especially for low elevation satellites (e.g., 10–20 degree), the accuracy is increased from tens of centimetres to a few centimetres. At user end, the positioning error in up direction with LIM has an obvious systematic deviation, and the fix rate of epoch is relatively low. This situation has been improved significantly after using ECDIM. The results of Tianjin Continuously Operating Reference System (TJCORS) show that in areas with small height difference, both methods have achieved high precision interpolation accuracy, and the positioning accuracy with ECDIM in up direction is improved by 21.2% compared with LIM.

Introducing the notion of a pseudoloxodrome, we generalise a single-heading navigation to conformally flat Riemannian manifolds, under the action of a perturbing vector field (wind, current) of arbitrary force. The findings are applied to time-optimal navigation with the use of the Euler–Lagrange equations. We refer to the Zermelo navigation problem admitting space and time dependence of both a perturbation and a ship's speed. The necessary conditions for single-heading time-optimal navigation are obtained and the pseudoloxodromes of minimum and maximum time are discussed. Furthermore, we describe winds which yield the pseudoloxodromic and loxodromic time extremals. Our research is also illustrated with the examples in dimension two emphasising the single-heading solutions among the time-optimal trajectories in the presence of some space-dependent winds.

As tugboats interact very closely with ships in restricted waters, the possibility of accidents increases in these operations. Despite the high accident possibility, there is a gap in studies on tugboat accidents. This study aims to analyse accidents involving tugboats using data mining. For this purpose, a tugboat accidents dataset consisting of a total of 496 accident records for the period from 2008 to 2019 was collected. Logistic regression and decision tree algorithms were implemented to the dataset. The results revealed that tugboat propulsion type is the most important and influential factor in the severity of tugboat accidents. The inferences drawn from these results could be beneficial for tugboat operators and port authorities in enhancing their awareness of the factors affecting tugboat accidents. In addition, the outputs of this study can be a reference for management units in developing strategies for preventing tugboat accidents and can also be used in effective planning for practicable prevention programmes and practices.

Global navigation satellite system (GNSS) receivers meet numerous challenges in a high-orbit environment, including weak and discontinuous signal, and time-varying strength. To resolve these issues and enhance reliability, an innovative adaptive vector tracking loop (VTL) scheme is proposed. Non-linear models of the VTL filter are established to calculate code phase and carrier frequency errors accurately. Based on this, a deep analysis has been developed on the measurement noise. To reduce the impact of the interdependent noises among channels in VTL, an adaptive VTL algorithm assisted by the variational Bayesian (VB) learning network is proposed to estimate the measurement noise and maintain the error convergence in the time-varying noise or signal outage conditions. Further, the implementation steps of the adaptive algorithm have been designed in detail. In particular, the carrier-to-noise power ratio (C/N0) estimation method is further employed to update the a prior probability density in case of change of tracking satellite. The simulation results indicate that the proposed VTL scheme with VB algorithm is a promising method to improve the accuracy and reliability of GNSS receivers significantly under a high-orbit degraded signal environment.

Scouring and sedimentation effects on the seabed induced by ship propellers during ship manoeuvring near harbour structures affect both structure stability and ship manoeuvring capabilities. This contribution proposes solutions at an operational level using the automatic identification system (AIS) and a bridge simulator. Two new alternative manoeuvres were designed and tested on a bridge simulator to obtain expected maximum scour depth and the results were compared with that of real manoeuvres (i) using mooring lines, and (ii) with tug assistance. A total of 42 test scenarios combining several manoeuvres and meteorological conditions were reproduced. Results confirmed a clear reduction in erosion depth with the alternative manoeuvres, with total reduction when using the tugboat. The presented methodology can be very useful to port authorities to prevent the effects of ship erosion on harbour infrastructures.

This study introduces a new real-time kinematic (RTK) positioning method which is suitable for baselines of different lengths. The method merges carrier-phase wide-lane, and ionosphere-free observation combinations (LWLC) instead of using pseudo-range, and carrier-phase ionosphere-free combination (PCLC), or single-frequency pseudo-range and phase combination (P1L1). In a first step, the double-differenced wide-lane ambiguities were calculated and fixed using the pseudo-range and carrier-phase wide-lane combination observations. Once the double-differenced wide-lane integer ambiguities were known, the wide-lane combined observations were regarded as accurate pseudo-range observations. Subsequently, the carrier-phase wide-lane, and ionosphere-free combined observations were used to fix the double-differenced carrier-phase integer ambiguities, achieving the final RTK positioning. The RTK positioning analysis was performed for short, medium, and long baselines, using the P1L1, PCLC, and LWLC methods, respectively. For a short baseline, the LWLC method demonstrated positioning accuracy similar to the P1L1 method, and performed better than the PCLC method. For medium and long baselines, the positioning accuracy of the LWLC method was slightly higher than those of the PCLC and P1L1 methods. In conclusion, the LWLC method provided high-precision RTK positioning results for baselines with different lengths, as it used high-precision carrier-phase observations with fixed ambiguities instead of low-precision pseudo-range observations.

For maritime safety and security, vessels should be able to predict the trajectories of nearby vessels to avoid collision. This research proposes three novel models based on similarity search of trajectories that predict vessels' trajectories in the short and long term. The first and second prediction models are, respectively, point-based and trajectory-based models that consider constant distances between target and sample trajectories. The third prediction model is a trajectory-based model that exploits a long short-term memory approach to measure the dynamic distance between target and sample trajectories. To evaluate the performance of the proposed models, they are applied to a real automatic identification system (AIS) vessel dataset in the Strait of Georgia, USA. The models' accuracies in terms of Haversine distance between the predicted and actual positions show relative prediction error reductions of 40·85% for the second model compared with the first model and 23% for the third model compared with the second model.

Geolocal is a new navigation system conceived and patented in Brazil, whose purpose is to be independent of other global navigation satellite systems (GNSS). It has an ‘inverted-GNSS’ configuration with at least four bases on the ground at known geodesic position coordinates and a repeater in space. Simulations were performed to determine the precision of Geolocal using different quantities and distributions of bases. They showed that this precision is enhanced when the quantity of bases increases, as long as the elevation angles of the new bases included are higher than the average and when the bases are evenly distributed around the repeater, but mainly when the time delay at the repeater is known in advance and when the measurement errors that generate uncertainties are reduced. The position dilution of precision (PDOP) was also calculated, confirming that precision is enhanced by the quantity of bases and by their distribution.

The time dispersion effect affects the accuracy of solar time difference of arrival (TDOA) navigation. In this celestial autonomous navigation, Mars's moons are reflecting celestial bodies, and their shape affects the TDOA dispersion model. In the modelling process of traditional methods, the moons of Mars (Phobos and Deimos) are regarded as points, which causes the model to be inaccurate. In order to solve these problems, we simplified the Mars's moons into ellipsoids or solid diamonds, and then established a TDOA model with the nonspherical Mars's moons as reflecting celestial bodies through differential geometry and geometric optics. Finally, we analysed the time dispersion caused by the Mars's moons in theory. Theoretical analysis and experiments show that the point model error is 5·66 km, and the 3D model error is within 70 m. Thus, the 3D TDOA model established in this paper is meaningful. In addition, the Sun–Mars-moons–spacecraft angle, solar flare, three-axis length, and attitude of the Mars's moons have a great effect on the dispersion profile, while the Mars's moons-to-spacecraft distance has a small effect.

During his 1869 expedition down the Green River and through the Grand Canyon, Major John Powell made astronomical observations using a sextant and artificial horizon to fix the locations of key points along the rivers that were only poorly known at the time. Latitude was obtained from the altitude of Polaris or meridian transits of stars or Saturn. Local mean time was determined from equal altitude observations of the Sun. The swamping of one of the expedition's small boats ruined the chronometers, meaning that they could not be used to keep Greenwich mean time and hence find longitude. As a substitute a series of lunar distance observations were undertaken. In this paper observations recorded in Powell's journal are reduced and analysed.

The star sensor field of view varies from several arc-minutes to 20 degrees, which directly determines the star vector orientation in the field of view (FOV). Although the relationship between star vector orientation in the FOV and attitude accuracy has been revealed, the influence mechanism of star vector orientation on the integrated navigation performance of a stellar inertial navigation system has not been analysed. In order to improve the integrated accuracy, the main errors such as star sensor installation error, gyro error and initial platform angle error should be estimated online. It is significant to study the influence mechanism of star vector orientation on estimation of the above errors. In this paper, the star sensor sensitivity and the geometry factor are defined to feature the difference between the optical axis direction and the non-optical axis direction. The formulised mechanism and quantification results between star vector orientation and integration attitude and error estimation accuracy are clearly given. Simulation and ground testing were conducted and it was found that the larger the star vector orientation along the optical axis, the better the error estimation accuracy. In contrast, the attitude accuracy is weakly sensitive to the orientation of the star vector in conditions of appropriate posture adjustment and star observation scheme. This conclusion can offer universal guidance for the design and evaluation of stellar inertial navigation systems with narrow field of view or large field of view star sensors.

The single initial Global Positioning System (GPS) has been expanded into multiple global and regional navigation satellite systems (multi-GNSS/RNSS) as the Global Navigation Satellite System (GLONASS) is restored and the BeiDou Navigation Satellite System (BDS), Galileo Satellite Navigation System (Galileo) and Quasi-Zenith Satellite System (QZSS) evolve. Using the differences among these five systems, the paper constructs a consolidated multi-GNSS/RNSS precise point positioning (PPP) observation model. A large number of datasets from Multi-GNSS Experiment (MGEX) stations are employed to evaluate the PPP performance of multi-GNSS/RNSS. The paper draws three main conclusions based on the experimental results. (1) The combined GPS/GLONASS/Galileo/BDS/QZSS presents the PPP with the shortest mean convergence time of 11·5 min, followed by that of GPS/GLONASS/Galileo/BDS (12·4 min). (2) The combined GPS/GLONASS/BDS/Galileo/QZSS shows the optimal PPP performance when the cut-off elevation angle is basically the same because of the rich observation data due to a large number of satellites. To be specific, for combined GPS/GLONASS/BDS/Galileo/QZSS, the PPP convergence percentage is 80·9% higher relative to other combined systems under 35° cut-off elevation angle, and the percentages of the root mean square values of PPP within 0–5 cm are enhanced by 80·5%, 81·5% and 87·3% in the North, East and Up directions relative to GPS alone at 35° cut-off elevation angle. (3) GPS alone fails to conduct continuous positioning due to the insufficiency of visible satellites at 40° cut-off elevation angle, while the kinematic PPP of multi-GNSS/RNSS remains capable of obtaining positioning solutions with relatively high accuracy, especially in the horizontal direction.