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.

This paper outlines the results of a project to develop and test an augmented reality smart phone application (‘app’) to aid the safety of navigation of leisure sailors with limited navigational skills. The app works in two modes: in the ‘turned off mode’ the app gives an alarm 30 seconds before the boat is predicted to ground. The navigator then immediately stops the boat, picks up the phone and, uses the app to view the surrounding water where NoGo areas less than 3 metres in depth are outlined in red. By panning the smart phone around, safe escape routes with deep water are visible. The prototype app was tested on a group of boat owners in western Norway with very good results, both from technical and usability perspectives. This report outlines the concept of operation of the app, details some of the difficulties encountered in its development and testing, specifies the issues that remain to be resolved to turn the concept into an effective system, and outlines future development plans.

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.

This paper presents a binocular vision-IMU (Inertial Measurement Unit) tightly-coupled structure based on a Minimum sigma set Square-Root Unscented Kalman Filter (M-SRUKF) for real time navigation applications. Though the M-SRUKF has only half the sigma points of the SRUKF, it has the same accuracy as the SRUKF when applied to the binocular vision-IMU tightly-coupled system. As the Kalman filter flow is a kind of square-root system, the stability of the system can be guaranteed. The measurement model and the outlier rejection model of this tightly-coupled system not only utilises the epipolar constraint and the trifocal tensor geometry constraint between the consecutive two image pairs, but also uses the quadrifocal tensor geometry among four views. The structure of the binocular vision-IMU tightly-coupled system is in the form of an error state, and the time updates of the state and the state covariance are directly estimated without using Unscented Transformation (UT). Experiments are carried out based on an outdoor land vehicle open source dataset and an indoor Micro Aerial Vehicle (MAV) open source dataset. Results clearly show the effectiveness of the proposed new mechanisation.

Finding one's geographical position (fix) without the use of a Global Navigation Satellite System (GNSS), which was common place before the establishment of the latter, could be tedious and/or inaccurate. Apart from sound knowledge of spherical trigonometry and navigational methods, it also requires the knowledge of the navigator's approximate or assumed position, the use of the current year's celestial bodies' ephemeris (Nautical Almanac), and graphical methods (Lines of Position – LOP) which sometimes can prove wanting in accuracy and/or challenging for the unaccustomed user. The method proposed here is based on sight reduction from two celestial bodies, and directly calculates the geographical position, both for stationary and moving observers (“running fix”) using easily available modern programmable calculating devices, without the need of the assumed position, graphical methods (LOP) or the current year's ephemeris, hence the term “stand-alone”. This self-contained method is implemented by the author in a software application, which can be easily used in a portable computer (for example, a smartphone). The results are considered satisfactorily accurate.

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.

An interplanetary autonomous navigation network, named the Internet of Spacecraft (IoS), is proposed in this paper to enable a Solar System-wide autonomous navigation capability for spacecraft. This network consists of two types of spacecraft, namely host and client spacecraft. The former provide the absolute reference for the whole network, and the latter determine their positions by communicating with the host spacecraft or other client spacecraft. To investigate the performance of IoS, a detailed application scheme that supports a flight from Earth to Mars is developed and analysed. IoS is not a simple extension of the navigation constellation. It is independent of the ground tracking system and the configuration of the network is flexible in that any spacecraft-installed identical device can be added to it. Moreover, client spacecraft whose positions have been determined can also be regarded as host spacecraft and provide further navigation information to others. This paper aims to provide technical support for future deep space exploration.

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.

To satisfy the needs of precise pin-point landing missions in deep space exploration, this paper proposes a method based on feature line extraction and matching to estimate the attitude and position of a lander during the descent phase. Linear equations for a lander's motion parameters are given by using at least three feature lines on the planetary surface and their two-dimensional projections. Then, by taking advantage of Singular Value Decomposition (SVD), candidate solutions are obtained. Lastly, the unique lander's attitude and position relative to the landing site are selected from the candidate solutions. Simulation results show that the proposed algorithm is able to estimate a lander's attitude and position robustly and quickly. Without an extended Kalman filter, the average errors of attitude are less than 1° and the average errors of position are less than 10 m at an altitude of 2,000 m. With an extended Kalman filter, attitude errors are within 0·5° and position errors are within 1 m at an altitude of 247·9 m.

High-precision underwater positioning must eliminate the influence of refraction artefacts. Since a Time Of Arrival - Global Navigation Satellite System Intelligent Buoys (TOA-GIB) system does not measure incident beam angles, common refraction correction methods cannot be directly used for refraction artefacts. An Equivalent Sound Speed (ESS) iteration method is proposed and is based on the transformation relations between depth, the ESS gradient and the incident beam angle. On this basis, a TOA/AOA-GIB system without a real-time Sound Speed Profile (SSP) is proposed to estimate the target position and the ESS gradient as unknown parameters. The results from a simulation experiment show that the positioning accuracy of a TOA/AOA-GIB system is better than 0·07% of water depth when the accuracy of the incident beam angle is 0·1°.

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.

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.

A novel fast adaptive-gain complementary filter algorithm is developed for Unmanned Aerial Vehicle (UAV) attitude estimation. This approach provides an accurate, robust and simple method for attitude estimation with minimised attitude errors and reduced computation. UAV attitude data retrieved from accelerometer data is transformed to the solution of a linearly discrete dynamic system. A novel complementary filter is designed to fuse accelerometer and gyroscope data, with a self-adjusted gain to achieve a good performance in accuracy. The performance of the proposed algorithm is compared with an Adaptive-gain Complementary Filter (ACF) and Extended Kalman Filtering (EKF). Simulation and experimental results show that the accuracy of the proposed filter has the same performance as an EKF in high dynamic operating conditions. Therefore, the proposed algorithm can balance accuracy and time consumption, and it has a better price/performance ratio in engineering applications.

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.

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.

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.

This paper proposes a dynamic aided inertial navigation method to improve the attitude accuracy for ocean vehicles. The proposed method includes a dynamic identification algorithm and the utilisation of dynamic constraints to derive additional observations. The derived additional observations are used to update the filters and limit the attitude error based on the dynamic knowledge. In this paper, two dynamic conditions, constant speed cruise and quasi-static, are identified and corresponding additional velocity and position observations are derived. Simulation and experimental results show that the proposed method can improve and guarantee the accuracy of the attitude. The method can be used as a backup method to bridge external information outages or unavailability. Both the features of independence of external support and integrity of the Inertial Navigation System (INS) are enhanced.

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.

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.