Code phase Global Navigation Satellite System (GNSS) positioning performance is often described by the Geometric or Position Dilution of Precision (GDOP or PDOP), functions of the number of satellites employed in the solution and their geometry. This paper develops lower bounds to both metrics solely as functions of the number of satellites, effectively removing the added complexity caused by their locations in the sky, to allow users to assess how well their receivers are performing with respect to the best possible performance. Such bounds will be useful as receivers sub-select from the plethora of satellites available with multiple GNSS constellations. The bounds are initially developed for one constellation assuming that the satellites are at or above the horizon. Satellite constellations that essentially achieve the bounds are discussed, again with value toward the problem of satellite selection. The bounds are then extended to a non-zero mask angle and to multiple constellations.

This paper describes a statistical method for learning and estimating the risk posed by other craft in the vicinity of a vessel and an overview of its possible spatial application, simulating how professional mariners perceive and assess such risk and using navigational data obtained from a standard integrated bridge. We propose a non-linear model for risk estimation which attempts to capture mariners' judgement. Questionnaire data has been collected that captures and quantifies mariners’ judgements of risk for craft in the vicinity, where each craft is described by measurements that can be obtained easily from the data already present in the ship's navigational equipment. The dataset has then been used for analysis, training and validating Ordered Probit models in order to obtain a computationally efficient data driven model for estimating the risk probability vector posed by other craft. Finally, we discuss how this risk model can be incorporated into decision making and path finding algorithms.

To improve the efficiency of multiple Autonomous Underwater Vehicles (multi-AUV) cooperative target search in a Three-Dimensional (3D) underwater workspace, an integrated algorithm is proposed by combining a Self-Organising Map (SOM), neural network and Glasius Bioinspired Neural Network (GBNN). With this integrated algorithm, the 3D underwater workspace is first divided into subspaces dependent on the abilities of the AUV team members. After that, tasks are allocated to each subspace for an AUV by SOM. Finally, AUVs move to the assigned subspace in the shortest way and start their search task by GBNN. This integrated algorithm, by avoiding overlapping search paths and raising the coverage rate, can reduce energy consumption of the whole multi-AUV system. The simulation results show that the proposed algorithm is capable of guiding multi-AUV to achieve a multiple target search task with higher efficiency and adaptability compared with a more traditional bioinspired neural network algorithm.

This paper is aimed at the risk assessment of operational safety for oil tankers. Based on the operational features of oil tankers and relevant literature, the Risk Factors (RFs) of operational safety were first identified. A revised risk matrix based on a fuzzy Analytical Hierarchy Process (AHP) approach was then proposed to assess the risk classes of the RFs. Finally, to validate the research model, the oil tanker fleet of Chinese Petroleum Corporation (CPC) in Taiwan was empirically investigated. The results can provide practical information for oil carriers to improve their ships' operational safety. Furthermore, the revised risk matrix may provide a theoretical reference for methodological researches in safety risk assessments.

The regional part of the current BeiDou navigation satellite system (BDS) consists of five Geostationary Earth Orbit (GEO) satellites, five Inclined Geosynchronous Satellite Orbit (IGSO) satellites and four Medium Earth Orbit (MEO) satellites. We examined three algorithms for BDS velocity estimation. In addition, the performance of velocity estimation using different BDS satellite combinations was analysed. Static tests demonstrated that velocity precision using Raw Doppler (RD) measurements was of the order of centimetres per second, whereas the carrier-phase-Derived Doppler (DD) measurements and Time-Differenced Carrier Phase (TDCP) method provided accuracies of the order of millimetres per second. Because of the irregularity of the satellites' distribution, three peaks exist on the north component in the 24-hour velocity series. Besides, the GEO satellites contribute significantly in velocity estimation and the satellites' geometry condition seriously declined when excluding GEO satellites. In kinematic tests, the root mean square of the velocity error derived by DD and TDCP both attained the centimetre per second level. Moreover, the precision of velocity determination with these three methods was degraded by the sudden acceleration of the vehicle.

A method is proposed for improving the accuracy and self-consistency of bathymetric maps built using an Autonomous Underwater Vehicle (AUV) to create precise prior maps for Terrain-Aided Navigation (TAN), when the Global Positioning System (GPS) or another precise location method is unavailable. This method consists of front-end and back-end. For the front-end, the AUV predicts the measurement of the bathymetry system through Terrain Elevation Measurement Extrapolation Estimation (TEMEE) and calculates the likelihood function using real measurements. After the final Inertial Navigation System (INS) error is obtained by communicating with sensor nodes, the process enters the back-end. A Terrain Correlation Correction Method (TCCM) and an Improved Terrain Correlation Correction Method (ITCCM) are proposed to solve the gradual distribution of the final INS error to each point on a path, and the accuracy of ITCCM was confirmed experimentally. Finally, a TAN simulation experiment was conducted to prove the importance and necessity of map correction using ITCCM. ITCCM was proven to be an effective and important method for correcting maps built using an AUV.

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.

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.

In this paper, we propose an algorithm for tuning both the kinematic and measurement noise Variance–Covariance (VCV) matrices to produce a more robust and adaptive Kalman filter. The proposed algorithm simultaneously considers both observation outliers and abrupt changes. This algorithm may be divided into two basic parts: 1. Robust estimation, from which the position components of the filtering estimates and the equivalent weight factor matrix can be obtained; and 2. Adaptive estimation, from which the adaptive kinematic noise VCV tuning matrix is calculated. To demonstrate the efficiency of our algorithm, we process a set of kinematic Global Positioning System (GPS) data received from a rover mounted on an aeroplane. The processing results are found to be very satisfactory, with observation outliers and abrupt changes detected and dealt with accordingly. The detailed calculation procedure for the adaptive VCV tuning matrix is also described.

This paper is concerned with the preliminary localisation, orbit determination and model-based path forecasting of space debris based on a robust procedure. In this work, an in-orbit observer utilises only relative bearing observations iteratively. To this end, the problem is first formulated in order to calculate the distance vector between the space debris and any orbiting observer. Afterwards, the obtained position vector is corrected through an Extended Kalman Filter (EKF) for shrinking the sensor and process errors and increasing robustness of the computations in the presence of uncertainties. After preliminary positioning, the related classical orbital elements are acquired via the predicted position and velocity vectors using a hybrid technique. Extensive simulations demonstrate the efficacy and robustness of the aforementioned method, and in particular it is verified that the proposed scheme is capable of producing a suitable solution for preliminary localisation and orbit determination of space debris based on the presented space-based observation, which is practical in phasing and chasing manoeuvres of any grabber space robot.

This paper describes a Multi-Criteria-Analysis (MCA)-based Decision Support System (DSS) developed for the management of incidents in maritime traffic. The developed DSS helps to organise a large quantity of information related to emergency management, spatial data and “live” data (radar data, weather forecasting data), to make it available to decision makers in a comprehensible and user-friendly way. Special care has been taken to model human Decision-Making (DM) processes during incident situations. Since the DM process is always multi-criterial, a Multi-Criteria Decision-Making (MCDM) method called Preference Ranking Organisation Method for Enrichment Evaluations (PROMETHEE) is used. However, a simplified variation of PROMETHEE II has been utilised to make results more understandable to non-expert users. The aim of this research is to incorporate effective DSS in human DM processes, thus reducing the possibility of making poor decisions. The concept of Web MCA-based DSS is presented as a case study: Web DSS developed for the east coast of the Adriatic Sea.

Zero velocity update (ZUPT) is widely discussed for error restriction in land vehicle Inertial Navigation Systems (INSs) and wearable pedestrian INSs to overcome the problems of Global Positioning System (GPS) unavailability in urban canyons or indoor scenarios. In this paper, an online smoothing method for ZUPT-aided INSs is presented. By introducing the Rauch–Tung–Striebel (RTS) smoothing method into the ZUPT-aided INS, position errors can be effectively restrained not only at stop points but during the whole trajectory. By integrating reverse navigation with a ZUPT smoother, the method realises forward and real-time processing. Compared with existing approaches, it can improve the position accuracy in real time without any other sensors, which is well suited for applications on high-accuracy navigation in GPS-challenging environments. Accuracy test results with different Inertial Measurement Units (IMUs) show that the developed method can significantly decrease position errors from hundreds or thousands of metres to below ten metres. During the whole trajectory, the online smoothing method ensures the maximum position errors at non-stop points can reach the same level of accuracy at stop points. A delay test result proves that the delay of the reverse online smoothing method proposed in this paper is much shorter than existing online smoothing methods.

This paper proposes a novel sensor fusion approach using Ultra Wide Band (UWB) wireless radio and an Inertial Navigation System (INS), which aims to reduce the accumulated error of low-cost Micro-Electromechanical Systems (MEMS) Inertial Navigation Systems used for real-time navigation and tracking of mobile robots in a closed environment. A tightly-coupled model of INS/UWB is established within the integrated positioning system. A two-dimensional kinematic model of the mobile robot based on kinematics analysis is then established, and an Auto-Regressive (AR) algorithm is used to establish third-order error equations of the gyroscope and the accelerometer. An Improved Adaptive Kalman Filter (IAKF) algorithm is proposed. The orthogonality judgment method of innovation is used to identify the “outliers”, and a covariance matching technique is introduced to judge the filter state. The simulation results show that the IAKF algorithm has a higher positioning accuracy than the KF algorithm and the UWB system. Finally, static and dynamic experiments are performed using an indoor experimental platform. The results show that the INS/UWB integrated navigation system can achieve a positioning accuracy of within 0·24 m, which meets the requirements for practical conditions and is superior to other independent subsystems.

The traditional Kalman filtering-based transfer alignment methods largely depend on prior information for initialisation. However, the initialisation process is hard to fulfil on a moving base. In this paper, a type of inertial measurement vector integration matching for optimisation-based transfer alignment and calibration is proposed to estimate the misalignment between the Master Inertial Navigation System (MINS) and Slave Inertial Navigation System (SINS), and main inertial sensor error parameters of SINS, including bias and scale factor error. In contrast to filter techniques, the proposed method has the capability of self-initialisation and provides a new idea to solve the alignment and calibration problem. No prior information is needed. Moreover, the integration time interval for the matching inertial measurement vector is selected by considering both the observation degree of inertial sensor error parameters and the noise effect. Simulation results demonstrate that the proposed method has faster convergence and is more accurate than Kalman filter techniques.

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.

Nonlinear least squares estimations have been widely applied in positioning. However, nonlinear least squares estimations are generally biased. As the Gauss-Newton method has been widely applied to obtain a nonlinear least squares solution, we propose an iterative procedure for obtaining unbiased estimations with this method. The characteristics of the linearization error are discussed and a systematic error source of the linearization error needs to be removed to guarantee the unbiasedness. Both the geometrical condition and the statistical condition for unbiased nonlinear least squares estimations are revealed. It is shown that for long-distance observations of high precision, or for a positioning configuration with the lowest Geometric Dilution Of Precision (GDOP), the nonlinear least squares estimations tend to be unbiased; but for short-distance cases, the bias in the nonlinear least squares solution should be estimated to obtain unbiased values by removing the bias from the nonlinear least squares solution. The proposed results are verified by the Monte Carlo method and this shows that the bias in nonlinear least squares solution of short-distance distances cannot be ignored.

Maritime traffic has significantly increased in recent decades due to its advantageous costs, delivery rate and environmental compatibility. With the advent of the new generation of marine radars, based on the solid-state transmitter technology that calls for much longer transmitted pulses, the interference problem can become critical. Knowing the positions and the heights of the ships, the mean number of the vessels in radar range can be estimated to evaluate the effects of their mutual radar interferences. This paper aims to estimate the probability density function of the mutual distances. The truncation of the density function within a limited area related to horizon visibility leads to a simple single-parameter expression, useful to classify the ships as either randomly distributed or following a defined route. Practical results have been obtained using Automatic Identification System (AIS) data provided by the Italian Coast Guard in the Mediterranean Sea.

A new integration of the acquisition and tracking modes is proposed for the integration of a Celestial Navigation System (CNS) and a Strapdown Inertial Navigation System (SINS). After the integration converges in the acquisition mode, it switches to the tracking mode. In the tracking mode, star pattern recognition is unnecessary and the integration is implemented in a cascaded filter scheme. A pre-filter is designed for each identified star and the output of the pre-filter is fused with the attitude of the SINS in the cascaded navigation filter. Both the pre-filter and the navigation filter are designed in detail. The measurements of the pre-filter are the positions on the image plane of one identified star. Both the starlight direction and its error are estimated in the pre-filter. The estimated starlight directions of all identified stars are the measurements of the navigation filter. The simulation results show that both the reliability and accuracy of the integration are improved and the integration is effective when only one star is identified in a period.

In a waist-worn Pedestrian Navigation System (PNS) based on Dead-Reckoning (DR), heading drift caused by Micro-Electro-Mechanical System (MEMS) gyro bias is an essential factor affecting DR accuracy. Considering the characteristics of pedestrian navigation and the poor bias repeatability of MEMS gyros, this paper presents a standing calibration method for MEMS gyro bias. The current gyro biases for each boot can be calibrated accurately in the initial stage before walking. Since the attitude angles calculated by the output data from magnetic sensor and accelerometers do not drift, this paper applies the reverse algorithm of attitude updating to calculate the angular velocities of human motion. Then the gyro biases at each moment can be acquired by subtraction operation between the measured angular velocities from gyros and the calculated angular velocities of human motion. Finally, in order to restrain the random error caused by sensor noise, the calculated biases in the initial stage are smoothed, and consequently the optimal estimate of current gyro biases after each boot can be obtained. Still and dynamic turntable experiments and a walking experiment are performed to compare and analyse the proposed method and the Zero Angular Rate Update (ZARU) method. Experimental results show that the proposed method can also calibrate the gyro bias accurately in the case of body swaying.

Ship surveillance is important in maritime management. Space-borne Synthetic Aperture Radar (SAR), High Frequency Surface Wave Radar (HFSWR) and the Automatic Identification System (AIS) are three main sensors for the ship surveillance of large maritime areas. Fusion of these sensors' measurements can produce an accurate ship image distribution in a surveillance area. Data association is fundamental to data fusion. A Maximum Likelihood (ML) association algorithm with multi-feature improvements is proposed to increase detection accuracy and reduce false alarms. The tested features are position, size, heading and velocity. First, the ship measurement model is established. Then, the problem of data association for SAR, HFSWR and AIS is formulated as a multi-dimensional assignment problem. In the data assignment process, Jonker-Volgenant-Castanon (JVC) and Lagrangian relaxation algorithms are applied. Simulation results show that the algorithm proposed here can improve the association accuracy compared with the Nearest Neighbour (NN) and the position-only ML algorithms, using the additional features of length and velocity. Real data experiments illustrate that the algorithm can enhance target identification and reduce false alarms.