This study aims to address the accuracy evaluation problem for rapid transfer alignment with the coexistence of large misalignment angles and uncertain observation noises. For the requirement of accuracy evaluation, complete information in terms of misalignment angles should be estimated during the alignment process. Thus, a fixed-interval smoothing approach is the core of solving this problem. In this paper, a new Divided Difference Filter (DDF)-based an Interacting Multiple Model Two-Filter Smoother (IMM-TFS) is developed to estimate the misalignment angles. The proposed DDF-based IMM-TFS releases the restriction of inverse nonlinearity by using the weighted statistical linearization regression method, and the resulting pseudo-linear model can be used for backward-time IMM filtering. The smoothing step takes into account the merging of estimations and the interaction of multiple models simultaneously. The new smoother is compared with the previous well-known methodologies in simulations. The results show that the DDF-based IMM-TFS can achieve better accuracy for misalignment angles estimation, and has a high efficiency for detecting the changes in a model.

For multi-Autonomous Underwater Vehicle (multi-AUV) system task assignment and path planning, a novel Glasius Bio-inspired Self-Organising Map (GBSOM) neural networks algorithm is proposed to solve relevant problems in a Three-Dimensional (3D) grid map. Firstly, a 3D Glasius Bio-inspired Neural Network (GBNN) model is established to represent the 3D underwater working environment. Using this model, the strength of neural activity is calculated at each node within the GBNN. Secondly, a Self-Organising Map (SOM) neural network is used to assign the targets to a set of AUVs and determine the order of the AUVs to access the target point. Finally, according to the magnitude of the neuron activity in the GBNN, the next AUV target point can be autonomously planned when the task assignment is completed. By repeating the above three steps, access to all target points is completed. Simulation and comparison studies are presented to demonstrate that the proposed algorithm can overcome the speed jump problem of SOM algorithms and path planning in the 3D underwater environments with static or dynamic obstacles.

The adoption of a robust collision avoidance module is required to realise fully autonomous Unmanned Surface Vehicles (USVs). In this work, collision detection and path planning methods for USVs are presented. Attention is focused on the difference between local and global path planners, describing the most common techniques derived from classical graph search theory. In addition, a dedicated section is reserved for intelligent methods, such as artificial neural networks and evolutionary algorithms. Born as optimisation methods, they can learn a close-to-optimal solution without requiring large computation effort under certain constraints. Finally, the deficiencies of the existing methods are highlighted and discussed. It has been concluded that almost all the existing method do not address sea or weather conditions, or do not involve the dynamics of the vessel while defining the path. Therefore, this research area is still far from being considered fully explored.

Solving the problem of ship weather routing has been always a goal of nautical navigation research and has been investigated by many scientists. The operation schedule of an oceangoing ship can be influenced by wave or wind disturbances, which complicate route planning. In this paper, we present a real-coded genetic algorithm to determine the minimum voyage route time for point-to-point problems in a dynamic environment. A fitness assignment method based on an individual's position in the sorted population is presented, which greatly simplifies the calculation of fitness value. A hybrid mutation operator is proposed to enhance the search for the optimal solution and maintain population diversity. Multi-population techniques and an elite retention strategy are employed to increase population diversity and accelerate convergence rates. The effectiveness of the algorithm is demonstrated by numerical simulation experiments.

This paper proposes a model for combined Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS) Real-Time Kinematic (RTK) positioning. The approach uses only one common reference ambiguity, for example, that of GPS L1, and estimates the pseudo-range and carrier phase system and frequency biases. The validations show that these biases are stable during a continuous reference ambiguity period and can be easily estimated, and the other estimated double-differenced ambiguities, such as those of GPS L2, BDS L1, and BDS L2, are not affected. Therefore, our approach solves the problems of a frequently changing reference satellite. In addition, because all the carrier phase observations use the same reference ambiguity, a relationship is established between the different systems and frequencies, and the strength of the combined model is thus increased.

This paper describes George Biddell Airy's almost completely unknown method of approximating an orthodromic arc (great circle arc) using a circular arc in the normal aspect Mercator projection of a sphere. In addition, it is demonstrated that the centre of the circle can be defined in at least two different ways, which yields slightly different results. Airy's approach is built upon in this paper. The method of computing coordinates of Airy's circle arc centre is described. The formulae derived in the paper can be used to calculate the length of Airy's approximation of the orthodromic arc connecting two points on the sphere and on the Mercator chart. Moreover, the actual length of the orthodromic arc on the sphere and on the Mercator chart can be computed using the formulae derived in this paper. The purpose of the paper is not to suggest an application of Airy's method in navigation, but to analyse Airy's proposal and to show that a great circle arc on a Mercator chart is close to a circular arc for distances which are not too great. This property can be useful in education, having in mind that the stereographic projection is the only one that maps any circle on a sphere onto a circle in the projection plane.

Cycle slip detection for single frequency Global Navigation Satellite System (GNSS) data is currently mainly based on measurement modelling or prediction, which cannot be effectively performed for kinematic applications and it is difficult to detect or repair small cycle slips such as half-cycle slips. In this paper, a new method that is based on the total differential of ambiguity and Least-Squares Adjustment (LSA) for cycle slip detection and repair is introduced and validated. This method utilises only carrier-phase observations to build an ambiguity function. LSA is then conducted for detecting and repairing cycle slips, where the coordinate and cycle slips are obtained successively. The performance of this method is assessed through processing short and long baselines in static and kinematic modes and the impact of linearization and atmospheric errors are analysed at the same time under a controlled variable method. The results indicate this method is very effective and reliable in detecting and repairing multiple cycle slips, especially small cycle slips.

This paper considers the effect of the biases in Global Positioning System (GPS) observations on satellite clock offset estimation. GPS triple-frequency satellite clock and reference observations are discussed. When the reference observation is selected and the corresponding satellite clock offset is computed, satellite clock offsets for all observations are obtained based on the computed satellite clock offset and the biases between the reference observation and other observations. The characteristics of these biases are analysed, and a service strategy for the GPS triple-frequency satellite clock offset is presented. To evaluate the computed GPS satellite clock offset, the performance in single-point positioning is validated. The positioning results show that the average relative improvements are about 20%, 28% and 19% for north, east and vertical components, when the Differential Code Bias (DCB) (P1-P2), DCB (P1-P5) and modelled Inter-Frequency Clock Bias (IFCB) are corrected. The effect of DCB (P1-P2), DCB (P1-P5) and modelled IFCB on the altitude direction is more evident than on the horizontal directions.

In the field of modernised Global Navigation Satellite System (GNSS) signal design, several Dual-frequency Constant Envelope Multiplexing (DCEM) methods have been recently proposed. However, the existing DCEM methods, such as Alternative Binary Offset Carrier (AltBOC), generalised AltBOC and Asymmetric Constant Envelope Binary Offset Carrier (ACE-BOC), are only applied in some special cases. In this paper, we present a unified DCEM design framework for GNSS signals. The existing DCEM methods can be unified in this framework. First, the signal components at two carrier frequencies are combined into two single-frequency constant envelope signals. Then, the linear sum of dual-frequency signals with non-constant envelopes is obtained. Finally, the linear sum is converted into the corresponding DCEM signal by solving an optimisation problem. The proposed design framework has no strict constraints on the number, power ratio and phase relationship of the signal components. Moreover, some special design cases under this framework are also analysed in detail. The analytical results show that the proposed design method can reach higher multiplexing efficiency compared with the existing methods. Based on the proposed method, we suggest a scheme to multiplex the BeiDou regional signals and global signals at the B2 frequency. The simulation results of correlation functions and Power Spectrum Density (PSD) verify the correctness and effectiveness of the proposed design method.

We examine the relation between fix error and the azimuthal distribution of lines of position by subsuming the distribution into a scalar form Q analogous to the nematic order parameter of statistical physics. It is shown in the least-squares approach that the error behaves as (1−Q2)−1/2. Simulation results are presented to demonstrate the control of Q as a strategy for fix improvement.

A Rotational Inertial Navigation System (RINS) redundant configuration is commonly adopted in high-accuracy marine navigation. Single-axis RINS and dual-axis RINS redundant configurations are good choices with single-axis RINS being a hot backup system, and are trade-offs between position accuracy, reliability as well as cost. However, lack of information fusion between systems is common. Therefore, a novel navigation information fusion method based on an augmented error state Kalman filter is proposed for a RINS redundant configuration. The azimuth gyro drift of a single-axis RINS whose influence cannot be averaged out by single-axis rotation can be estimated, whereby the deterministic position error can be predicted and compensated. Hence, the position accuracy in the event of dual-axis RINS failure can be guaranteed by improving the performance of a single-axis RINS. In addition, an online performance evaluation method is proposed to select the better performance dual-axis RINS as master RINS in a triple RINS configuration, including two sets of dual-axis RINS and a single-axis RINS, which is used in some particularly high reliability applications. Semi-physical simulations and experiments show the proposed method works well.