With the evolving Global Navigation Satellite System (GNSS) landscape, the International GNSS Service (IGS) has started the Multi-GNSS Experiment (MGEX) to produce precise products for new generation systems. Various analysis centres are working on the estimation of precise orbits, clocks and bias for Galileo, Beidou and Quasi-Zenith Satellite System (QZSS) satellites. However, at the moment these products can only be used for post-processing applications. Indeed, the IGS Real-Time service only broadcasts Global Positioning System (GPS) and Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS) corrections. In this research, a simulator of multi-GNSS observations and real-time precise products has been developed to analyse the performance of GPS-only, Galileo-only and GPS plus Galileo Precise Point Positioning (PPP). The error models in the simulated orbits and clocks were based on the difference between the GPS Real-Time and the Final products. Multiple scenarios were analysed, considering different signals combined in the Ionosphere Free linear combination. Results in a simulated open area environment show better performance of the Galileo-only case over the GPS-only case. Indeed, up 33% and 29% of improvement, respectively, in the accuracy level and convergence time can be observed when using the full Galileo constellation compared to GPS. The dual constellation case provides good improvements, in particular in the convergence time (47% faster than GPS). This paper will also consider the impact of different linear combinations of the Galileo signals, and the potential of the E5 Alternative Binary Offset Carrier (AltBOC) signal. Even though it is significantly more precise than E5a, the PPP performance obtained with the Galileo E1-E5a combination is either better or similar to the one with Galileo E1-E5. The reason for this inconsistency was found in the use of the ionosphere free combination with E1. Finally, alternative methods of ionosphere error mitigation are considered in order to ensure the best possible positioning performance from the Galileo E5 signal in multi-frequency PPP.

Markley variables have advantages of slow variation, easy numerical integration and high precision in describing the attitude of spinning spacecraft. Previous attitude estimation methods based on Markley variables for spinning spacecraft usually employ a sun vector from the sun sensor, a magnetic vector from the magnetometer, or the angular rate from the gyro as the measurement. This paper proposes a Markley variables-based attitude estimation method using optical flow and a star vector from a star sensor as the measurement, where optical flow provides rate information and the star vector provides direction information. This method can estimate the direction of the spin axis and spin angular rate very well by using only one star sensor. In addition, the star sensor has higher accuracy than the traditional sun sensor and magnetometer, and the star sensor can also replace the gyro in case the gyro is out of action. The impact factors of this method are also analysed, which include spin angular rate, spin axis orientation and spacecraft moment of inertia tensor error.

Maritime accident statistics reveal that ship collisions are among the most frequent and severe accidents. The same statistics indicate that most of them are caused by human error, mainly due to breaches of the International Regulations for Preventing Collisions at Sea (COLREGs) and to the lack of communication between ships. There are also special situations where there is some ambiguity in the application of the COLREGs. In such occasions, and if there is no communication between the ships involved, compliance with the Rules may still end up in a collision. This article brings a new approach to Collision Avoidance Systems (CAS) and presents the earliest stages in the development of safety functions for the reduction of ship-to-ship collision risk on the high seas. These functions will help the concerned ships achieve coordinated compliance with the COLREGs. Functional safety standards are applied and, in their implementation, real, accessible electronic programmable systems (hardware and software) will be used.

A new acoustic positioning method for Autonomous Underwater Vehicles (AUV) that uses a single underwater hydrophone is proposed in this paper to solve problems of Long Baseline (LBL) array laying and communication synchronisation problems among all hydrophones in the traditional method. The proposed system comprises a Strapdown Inertial Navigation System (SINS), a single hydrophone installed at the bottom of the AUV and a single underwater sound source that emits signals periodically. A matrix of several virtual hydrophones is formed with the movement of the AUV. In every virtual LBL window, the time difference from the transmitted sound source to each virtual hydrophone is obtained by means of a Smooth Coherent Transformation (SCOT) weighting cross-correlation in the frequency domain. Then, the recent location of the AUV can be calculated. Simulation results indicate that the proposed method can effectively compensate for the position error of SINS. Thus, the positioning accuracy can be confined to 2 m, and the method achieves good applicability. Compared with traditional underwater acoustic positioning systems, the proposed method can provide great convenience in engineering implementation and can reduce costs.

Radiolocation systems for aviation based on Multi-Lateration (MLAT) typically use a set of synchronised ground sensors to receive radio signals broadcast by onboard transmitters. In most cases, the sensor synchronisation in Wide Area Multi-Lateration Systems (WAM) is provided by Global Navigation Satellite System (GNSS) receivers. However, in the case of synchronisation failure, there is still a possibility to estimate the coordinates of the tracked aircraft by using the measurements of the time of arrival taken by non-synchronised sensors. The article presents the principle of operation and equations for calculating the coordinates of an aircraft in an asynchronous multi-lateration system, together with the results of a computer simulation allowing comparison of the accuracy of position estimation between the asynchronous and the typical, synchronous MLAT. This paper contains also some comments on the required stability of the clock source for the sensors working in an asynchronous MLAT system.

Modern ship simulators enable simulations of reality using available environment and ship models. When choosing a specific vessel from a catalogue, however, it is not always immediately apparent as to how true a simulation is to the original vessel. Its makers are required only to have software certificates, which does not ensure the exact modelling of a ship in the simulation. This paper presents research in continuation of previous work presenting a general methodology for the evaluation of the degree of accuracy of a simulated ship model compared to its real-world counterpart. In this paper, the results are shown of a comparative analysis based on actual measurements with the use of one of the methods of multi-criteria analysis. Furthermore, the methodology for the construction of ship models is presented. The paper concludes with a test verifying the accuracy of the assumptions.

Since the descriptors based on Three-Dimensional (3D) Zernike moments are robust to geometric transformations and noise, they have been proposed for terrain matching. However, terrain matching algorithms based on 3D Zernike Moments (3DZMs) are often difficult to implement in practice since they are computationally intensive. This paper presents a more efficient real-time terrain matching algorithm based on 3DZMs for land applications. Two efficient methods based on coordinate transformation and symmetry are proposed to compute the geometric moments. The impact of the sample difference on the matching result due to heading angle is investigated to prove the feasibility of using a circular template. Consequently, the terrain feature vectors of the reference map can be computed off-line with the circular template to significantly reduce on-line computation. Numerical experiments on a real digital elevation model demonstrate that the proposed algorithm is robust to the heading angle and can be implemented for real-time terrain matching operations.

A new unambiguous tracking technique based on combined correlation functions for sine Binary Offset Carrier (BOC) signals is proposed in this paper. The key to this method is to exploit two types of local reference signals: the BOC signal and a linear combination of a series of BOC signals with different delays. They are both correlated with the received signals. Then, a correlation function without any positive side peaks is obtained by multiplying the two correlation results to make tracking completely unambiguous. Theoretical analysis and simulation in the tracking stage show that the proposed method has the best code tracking accuracy among the method tracking BOC signals like Binary Phase-Shift Keying signals (BPSK-LIKE), the Pseudo correlation function based Unambiguous Delay Lock Loop (PUDLL), Symmetrical Pulse Ambiguity Removing (SPAR) technique, the method proposed by Shen Feng (SF) and the two methods proposed by Yan Tao (YT-V1 and YT-V2). In multipath environments, the proposed method has the best anti-multipath performance of all the tracking methods mentioned above. In conclusion, the proposed method can completely eliminate ambiguity and has significant performance advantages compared with the methods mentioned above.

The Carrier-Phase (CP) technique used in the Global Positioning System (GPS) has proved to be a useful spatial tool for remote precise time transfer. Galileo is a Global Navigation Satellite System like GPS. However, currently, given the low number of satellites at any one observation epoch, Galileo's accuracy and continuity of time transfer leave much to be desired. To achieve better performance of time transfer for Galileo, this study has developed a new approach for Galileo CP time transfer, using prior constraint information such as precise coordinates and troposphere zenith delay constraints. The new approach was applied for precise time transfer in real-time mode and post-processed mode for short baseline and long baseline observations. For the short baseline time link in real-time mode, compared with the standard Galileo CP, the standard deviation improved by 51·4% for the troposphere zenith delay constraint, 47·6% for the station coordinates constraint, and 49·5% when considering both constraints simultaneously. At a 10,000 s time interval, in comparison to the standard CP, the three constraint approaches show stable results as well as improvements of nearly an order of magnitude. In post-processed mode, the constraint approach for Galileo time transfer showed little improvement compared to the standard CP technique for both the short baseline and long baseline time links.

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.

In order to utilise the position and attitude information of a Celestial Navigation System (CNS) to aid a Strapdown Inertial Navigation System (SINS) and make it possible to achieve long-range and high-precision navigation, a new SINS/CNS integrated navigation scheme based on overall optimal correction is proposed. Firstly, the optimal installation angle of the star sensor is acquired according to the geometric relationship between the refraction stars area and the star sensor's visual field. Secondly, an analytical method to determine position and horizontal reference is introduced. Thirdly, the mathematical model of the SINS/CNS integrated navigation system is established. Finally, some simulations are carried out to compare the navigation performance of the proposed SINS/CNS integrated scheme with that of the traditional gyro-drift-corrected integration scheme. Simulation results indicate that in the proposed scheme, without the aid of SINS, CNS can provide attitude and position information and the errors of the SINS are able to be estimated and corrected efficiently. Therefore, the navigation performance of the proposed SINS/CNS scheme is superior to that of a more traditional scheme in long-range flight.

Tropospheric delay is one of the main error sources in Global Navigation Satellite System (GNSS) Precise Point Positioning (PPP). Zenith Hydrostatic Delay (ZHD) accounts for 90% of the total delay. This research focuses on the improvements of ZHD from tropospheric models and real meteorological data on the PPP solution. Multi-GNSS PPP experiments are conducted using the datasets collected at Multi-GNSS Experiments (MGEX) network stations. The results show that the positioning accuracy of different GNSS PPP solutions using the meteorological data for ZHD correction can achieve an accuracy level of several millimetres. The average convergence time of a PPP solution for the BeiDou System (BDS), the Global Positioning System (GPS), Global Navigation Satellite System of Russia (GLONASS), BDS+GPS, and BDS+GPS+GLONASS+Galileo are 55·89 min, 25·88 min, 33·30 min, 20·50 min and 15·71 min, respectively. The results also show that atmospheric parameters provided by real meteorological data have little effect on the horizontal components of positioning compared to the meteorological model, while in the vertical component, the positioning accuracy is improved by 90·6%, 33·0%, 22·2% and 19·8% compared with the standard atmospheric model, University of New Brunswick (UNB3m) model, Global Pressure and Temperature (GPT) model, and Global Pressure and Temperature-2 (GPT2) model and the convergence times are decreased 51·2%, 32·8%, 32·5%, and 32·3%, respectively.

A high-precision line-of-sight extraction technique is essential for autonomous optical navigation during the Mars approach phase. To support future Mars exploration missions, an optical image simulation system is a necessary ground verification facility for Mars image generation and line-of-sight extraction algorithm tests. In this paper, an optical image generation procedure is first developed according to projection relationships, reference flight profiles and camera parameters. Next, a hybrid image processing and subpixel-level line-of-sight extraction algorithm is proposed through modification of moment-based sub-pixel edge detection and improvement of direct least-square fitting approaches. Finally, an optical image simulation system is established, and the experimental results show that the proposed procedure can effectively simulate the optical image in the field-of-view of a Mars spacecraft, and the hybrid extraction algorithm can obtain high-precision Mars centroid information.

This paper describes a fully autonomous real-time in-motion alignment algorithm for Strapdown Inertial Navigation Systems (SINS) in land vehicle applications. Once the initial position is available, the vehicle can start a mission immediately with accurate attitude, position and velocity information determined within ten minutes. This is achieved by two tightly coupled stages, that is, real-time Double-vector Attitude Determination Coarse Alignment (DADCA) and Backtracking Fine Alignment (BFA). In the DADCA process, the vehicle motion is omitted to roughly estimate the attitude at the very start of the alignment. Meanwhile, attitude quaternions and velocity increments are extracted and recorded. The BFA process utilises the stored data and exploits the Non-Holonomic Constraints (NHC) of a vehicle to obtain virtual velocity measurements. A linear SINS/NHC Kalman filter with mounting angles as extended states is constructed to improve the fine alignment accuracy. The method is verified by three vehicle tests, which shows that the accuracy of alignment azimuth is 0·0358° (Root Mean Square, RMS) and the positioning accuracy is about 15 m (RMS) at the end of the alignment.

Global Navigation Satellite Systems (GNSSs) are easily influenced by the external environment. Signals may be lost or become abnormal thereby causing outliers. The filter gain of the standard Kalman filter of a loosely coupled GNSS/inertial navigation system cannot change with the outliers of the GNSS, causing large deviations in the filtering results. In this paper, a method based on a χ2-test and a dynamically adjusting filter gain method are proposed to detect and separately to suppress GNSS observation outliers in integrated navigation. An indicator of an innovation vector is constructed, and a χ2-test is performed for this indicator. If it fails the test, the corresponding observation value is considered as an outlier. A scale factor is constructed according to this outlier, which is then used to lower the filter gain dynamically to decrease the influence of outliers. The simulation results demonstrate that the observation outlier processing method does not affect the normal values under normal circumstances; it can also discriminate between single and continuous outliers without errors or omissions. The impact time of outliers is greatly reduced, and the system performance is improved by more than 90%. Experimental results indicate that the proposed methods are effective in suppressing GNSS observation outliers in integrated navigation.

As the geographical meridians converge rapidly, traditional inertial navigation methods fail in the polar regions. Classic transversal navigation methods can address the problem by transversal rotation of the original north and south poles, but this can introduce errors based on the spherical Earth model. To reduce the principle errors, some fruitful research work using an ellipsoidal Earth model has been done. Under the ellipsoid Earth model, transversal navigation for polar region becomes a complex coupling problem. Considering the coupling of the three-dimensional motion, a more rigorous mechanism for transversal navigation using an ellipsoidal Earth model is proposed. Starting from the relationship between Euclidean coordinates and spherical coordinates, the main equations of transversal polar navigation based on an ellipsoidal Earth model are derived in detail. Complete mechanical arrangements of attitude, position and velocity calculation are presented. The new derivation in this paper completely avoids solving the ellipsoidal radius. Numerical results indicate that the proposed transversal navigation mechanism can outperform the traditional method, especially in the condition of vertical motion.

This paper comprehensively investigates the fault exclusion problem in multi-constellation Global Navigation Satellite Systems (GNSS). In future GNSS, the heightened likelihood of fault detection events will cause more interruptions in the continuity of the navigation operation. The main contribution of this paper is to establish the theoretical basis to quantify the contributions of fault events on continuity risk, therefore allowing us to assess the desired exclusion function performance based on specific continuity requirements. Accordingly, a new real-time exclusion algorithm is developed, for which the upper bounds on integrity risks are rigorously derived. Using the new method, performance is comprehensively investigated for two important civil aircraft navigation operations using various numbers of constellations. We show that high service availability can be achieved for both operations.