Procedures based on solutions of the direct and inverse geodetic problems are presented and their application in orthodromic and loxodromic navigation is analysed. They can be used in traditional navigation during a route planning and during sailing on the planned route in real time. The optimal division of orthodromes during planning and locally predicted short loxodromes during sailing – which allow orthodromic navigation also in manual steering – are proposed.

In this paper, a fault-tolerant velocity estimation method is proposed for quadrotors in a GPS denied environment. A novel filter is developed in light of the quadrotor model and measurements from optical flow and inertial sensors. The proposed filter is capable of detecting and isolating the optical flow sensor faults, by which the velocity estimation accuracy and stability will be improved. It is also demonstrated that the wind velocity is observable in the proposed filter. Therefore, the new filter can also be implemented in a windy environment, which is a significant improvement to the previous model-aided inertial sensor estimator. At the end, some simulations are carried out to verify the advantages of our method.

This paper focuses on depth trajectory tracking control for a Remotely Operated Vehicle (ROV) with dead-zone nonlinearity and saturation nonlinearity of thruster; an adaptive sliding mode control method based on neural network is proposed. Through the analysis of dead-zone nonlinearity and saturation nonlinearity of thruster, the depth trajectory tracking control system model of a ROV which uses thruster control signals as system input has been established. According to the principle of sliding mode control, an adaptive sliding mode depth trajectory tracking controller is built by using three-layer feed-forward neural network for online identification of unknown items. The selection method and update laws of the control parameters are also given. The uniform ultimate boundedness of trajectory tracking error is analysed by Lyapunov theorem. Finally, the effectiveness of the proposed method is illustrated by simulations.

In Strapdown Inertial Navigation System (SINS)/Odometer (OD) integrated navigation systems, OD scale factor errors change with roadways and vehicle loads. In addition, the random noises of gyros and accelerometers tend to vary with time. These factors may cause the Kalman filter to be degraded or even diverge. To address this problem and reduce the computation load, an Adaptive Two-stage Kalman Filter (ATKF) for SINS/OD integrated navigation systems is proposed. In the Two-stage Kalman Filter (TKF), only the innovation in the bias estimator is a white noise sequence with zero-mean while the innovation in the bias-free estimator is not zero-mean. Based on this fact, a novel algorithm for computing adaptive factors is presented. The proposed ATKF is evaluated in a SINS/OD integrated navigation system, and the simulation results show that it is effective in estimating the change of the OD scale factor error and robust to the varying process noises. A real experiment is carried out to further validate the performance of the proposed algorithm.

This paper presents a framework for a strapdown Inertial Navigation System (INS) algorithm design by using Lie group and Lie algebra. The general way to solve Lie group differential equations is introduced. Investigations reveal that this general Lie group method provides a simpler unified way to solve differential equations involving direction cosine matrix, quaternion and dual quaternion, which are widely used in INS algorithm design. Furthermore, we also present a new INS algorithm based on the Special Euclidean group se(3) under the guidelines of Lie group method. Analyses show that se(3) algorithm has the same accuracy as a dual quaternion algorithm, this is also justified by numerical simulations. Though the se(3) algorithm has no improvements in accuracy, the general Lie group method used in the design process shows its brevity and uniformity.

Navigational error accounts for half of the accidents and serious incidents in close to shore maritime transport in Norway predominantly due to the rapidly changing weather conditions and the dangerous nature of the narrow inshore waters found along the Norwegian coast. This creates a dependence on Differential Global Positioning System (DGPS) use and any disruption to this service can lead to an increased accident rate. The aim of this paper is to research the jamming vulnerability of existing maritime receivers and to understand if an upgrade to a multi-constellation or multi-frequency receiver would improve system resilience. The novelty of this work is a comparison of jamming resilience between different combinations of multiple constellations (GPS and Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS)) and multi-frequency Global Navigation Satellite System (GNSS) signals. This paper presents results from GNSS jamming trials conducted in the northern part of Norway, confirming previous research and indicating that typical maritime GPS receivers are easy to jam and may produce erroneous positional information. Results demonstrate that the single frequency multi-constellation receivers offer better jamming resilience than multi-frequency (L1 + L2) GPS receivers. Further, the GLONASS constellation demonstrated a better resilience than GPS. Results demonstrate a known correlation between GPS L1 and L2 frequencies, as well as a probable over-dependence on GPS for signal acquisition, meaning that no signal can be received without GPS L1 present. With these limitations in mind, the authors suggest that the most economic update to the single frequency GPS receivers, currently used for maritime applications, should be multi-constellation GPS + GLONASS receivers. This solution is cheaper and it also offer better jamming resistance for close to shore navigation than dual frequency receivers.

This paper reports the results of the first three in a series of experiments on tactile perception which form part of a larger project on tactile perceptions and spatial representations and the design of tactile interfaces for mobility devices for blind, partially sighted and deafblind people. The results indicate the potential of tactile interfaces, including to support environmental exploration and mobility. The participants showed reasonably good ability to determine the direction of motion of an arrow, with best recognition rates in the up and right directions. They showed reasonably good ability to use a tactile interface to detect and avoid obstacles after a very short learning period and more limited ability to learn and remember an environmental representation using information from a tactile interface and walking through the environment without specific instructions.

Automatic Dependent Surveillance Broadcast (ADS-B) Out supports various ground applications including Air Traffic Control (ATC) surveillance in radar airspace, non-radar airspace and on the airport surface. In addition, the capability of aircraft to receive ADS-B Out messages from other aircraft within their coverage (ADS-B In) enables enhanced airborne surveillance applications. The requirements of the application vary depending on its safety-criticality. More stringent applications will require higher levels of performance. It is therefore critical that the ADS-B system performance is measured against the most stringent application it is designed for. This paper reviews the various enhanced airborne surveillance applications and the required ADS-B information to support them. It identifies the ADS-B based applications required for Air Traffic Management (ATM) modernisation under the SESAR/NextGen programs. It discusses existing ADS-B Out versions and their capabilities. A mapping exercise is undertaken to assess the credibility of the ADS-B system performance to support the functionalities and requirements of the various enhanced airborne surveillance applications and establish those that require further research and development, highlighting some of the key challenges.

Relative position awareness is a vital premise for the implementation of emerging intelligent transportation systems. However, commercial Global Satellite Navigation Systems (GNSS) receivers do not satisfy the requirements of these applications. Fortunately, Cooperative Positioning (CP) systems, based on inter-vehicle communications, have improved performance of relative positioning in a Vehicular Ad Hoc Network (VANET). CP techniques rely primarily on measurements from the Global Positioning System (GPS) to deliver measurements or positions that describe the location of individual vehicles. In urban environments, the reduced quality or complete unavailability of GPS measurements challenges the effectiveness of any CP algorithm. In this paper, a new enhanced tightly–coupled CP technique is presented by adding the measurements from low-cost inertial sensors and the Doppler shift of the carrier of Dedicated Short-Range Communications (DSRC) signals. In the enhanced CP method proposed here, vehicles communicate their Inertial Measurement Unit (IMU) data and GPS measurements. Each vehicle fuses the GPS measurements and IMU data and the inter-node range-rates based on the Doppler shift of the carrier of DSRC signals. Based on analytical and experimental results, in a full GPS coverage environment, the new tight integration CP outperforms tight CP with Inertial Navigation System (INS), tight CP and differential GPS by at least by 6%, 15%, and 28%, respectively. In a GPS outage, the performance improvement can be up to 60%, 55%, and 66% respectively.

Measurement bias and lack of terrain features often cause false peaks during underwater terrain matching positioning, that is, there is more than one peak near the real position. Previous methods to address this problem have increased the number of measurement beams, but this also increases the data processing time and energy consumption. At the same time, the ratio of measured information that is used does not increase. In other words, we should increase the ratio of measured information that is used, not simply increase the amount of information that is measured. Conventional matching algorithms only use the height of nodes without considering surface information, which is composed of height and the position of multiple nodes in three-dimensional space. Multi-beam sonar can obtain the three-dimensional distribution of terrain nodes. This node information is not just a height sequence, as it is used in previous methods. If we consider the nodes as a three-dimensional distribution of points with height and position information, this increases the matching position information and more of the terrain features can be extracted from the same measured data. Hence, in this paper, a terrain positioning method called the Node Multi-information Fusion (NMIF) is presented. This method focuses on improving the stability and accuracy degraded by bias in the Digital Elevation Map (DEM), terrain repeatability, and other factors. First, the concept of a Single Node Data Packet (SNDP) is introduced. The SNDP includes elevation and surface information surrounding the node, such as roughness, gradient, and slope. This additional topographic feature information improves the robustness and accuracy of the system. A computer simulation using actual ocean bottom topography verifies the advantages of the proposed NMIF algorithm.

In order to achieve high accuracy of autonomous navigation for Mars probes, an integrated navigation method using X-ray pulsar measurement and optical data of viewing Martian moons is proposed. For single X-ray pulsar measurement on board a Mars probe, navigation accuracy is low due to its poor observability. On the other hand, Phobos and Deimos, two natural moons of Mars, are important optical navigation information sources available for Mars missions. However, the Martian moons ephemeris bias and the differences between barycentre and centre of brightness of Martian moons will result in low navigation accuracy. The method of integrated navigation using X-ray pulsar measurement and optical data of viewing Martian moons can overcome the defect and achieve accurate navigation. Two sequential orbit determination algorithms, Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), are compared. The simulation results show this method can obtain high autonomous navigation accuracy during the phase of a probe orbiting Mars.

A region tracking fault tolerant control approach based on backstepping technique is proposed for Autonomous Underwater Vehicles (AUV). The proposed approach aims at driving tracking error to reach into the desired region in presence of ocean current disturbance, modelling uncertainty, unknown thruster faults and thruster amplitude and rate saturation constraints. At first, a type of piecewise and differential Lyapunov function is constructed to achieve region tracking control in the frame of backstepping technique. Then, the paper analyses and acquires the bound structures of the lumped uncertainty (including ocean current disturbance and model uncertainty) and the variation of thruster distribution matrix caused by unknown thruster faults, respectively. An adaptive technique is used to estimate the unknown coefficients in the above bound structures. In addition, an adaptive adjustment scheme for the desired trajectory is developed to achieve region tracking control with thruster amplitude and rate saturation constraints. The stability of the closed-loop system is analysed based on Barbalat's lemma. Finally, simulations and pool-experiments are presented to illustrate the effectiveness of the proposed method.

The correct ambiguity resolution between reference stations is the core issue of the whole Network Real-Time Kinematic (RTK) technology. Aimed at long fixed time and low reliability of the low elevation angle satellite ambiguity resolution during the initialisation of the Network RTK system, a three-step algorithm is proposed in this paper. Firstly, the double difference wide-lane ambiguities are fixed on the basis of the Melbourne-Wubbena (MW) method. Secondly, the double difference L1 carrier phase ambiguities of the high elevation angle satellites are fixed rapidly based on the ionosphere-free combination model. Thirdly, the corresponding ambiguities of the satellites with low elevation angles are solved with restrictions from the double difference tropospheric information, which is obtained from observations of the high elevation angle satellites. Based on this algorithm, an overall scheme of the ambiguity resolution during the initialisation process of the Network RTK system is designed. Results from Global Positioning System (GPS)/Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS) data demonstrate that the three-step algorithm can reduce the ill-posed problems of the observation model effectively. Moreover, the speed and accuracy performances of the ambiguity resolution for the low elevation angle satellites using the proposed algorithm are better than those of the conventional method.

An assessment of the navigational accuracy of the Mercator world map of 1569 is made, aimed at better understanding how the information was adapted from the contemporary cartography. At the time the map was engraved, navigational charts were constructed on the basis of astronomically-observed latitudes, magnetic courses and estimated distances between places. Before this information could be incorporated into the new world map it should be first transformed in such a way that the longitudinal spacings between places were restored to their correct values, as defined on the surface of the Earth. The question of whether Mercator performed such transformations or just considered that the positions were approximately correct has hitherto never been addressed in the literature. It is demonstrated in this article that Mercator was not fully aware of the complexity of the contemporary charts – which he considered to implicitly comprise a square grid of meridians and parallels – and that all planimetric information was directly imported to the novel world map without correction. It is further shown that the Mercator projection was not compatible with the navigational methods of the time.

Knowledge of forces and yaw moments which exist between a pair of vessels moving parallel to each other is crucial to the design of their automatic motion control system. Studies involving measurements of forces and moments occurring between a pair of ships were undertaken. The research was carried out on the basis of two real floating training ship models made at 1:24 scale in real conditions on the Silm Lake in Ilawa Kamionka. As a result, suction forces and yaw moments occurring between the pair of vessels calculated according to semi-empirical formula were verified. It was found that the process of overtaking and parallel motion (which is a quasi-stationary motion) could not be modelled in the same way. Nevertheless, the results confirmed the presence of forces and moments with values similar to those in the catch-up and parallel motion phases during the ships’ overtaking manoeuvre. Thanks to this confirmation, it was possible to use the results of the analytical calculation for the catch-up phase during design of the ships' parallel motion automatic control system.

Mapping global shipping density, including vessel density and traffic density, is important to reveal the distribution of ships and traffic. The Automatic Identification System (AIS) is an automatic reporting system widely installed on ships initially for collision avoidance by reporting their kinematic and identity information continuously. An algorithm was created to account for errors in the data when ship tracks seem to ‘jump’ large distances, an artefact resulting from the use of duplicate identities. The shipping density maps, including the vessel and traffic density maps, as well as AIS receiving frequency maps, were derived based on around 20 billion distinct records during the period from August 2012 to April 2015. Map outputs were created in three different spatial resolutions: 1° latitude by 1° longitude, 10 minutes latitude by 10 minutes longitude, and 1 minute latitude by 1 minute longitude. The results show that it takes only 56 hours to process these records to derive the density maps, 1·7 hours per month on average, including data retrieval, computation and updating of the database.