This contribution covers precise (cm-level) relative Global Navigation Satellite System (GNSS) positioning for which the baseline length can reach up to a few hundred km. Carrier-phase ambiguity resolution is required to obtain this high positioning accuracy within manageable observation time spans. However, for such long baselines, the differential ionospheric delays hamper fast ambiguity resolution as based on current dual-frequency Global Positioning System (GPS). It is expected that the modernization of GPS towards a triple-frequency system, as well as the development of Galileo towards a full constellation will be beneficial in speeding up long-baseline ambiguity resolution. In this article we will predict ambiguity resolution success rates for GPS+Galileo for a 250 km baseline based on the ambiguity variance matrix, where the Galileo constellation is simulated by means of Yuma almanac data. From our studies it can be concluded that ambiguity resolution will likely become faster (less than ten minutes) in the case of GPS+Galileo when based on triple-frequency data of both systems, however much shorter times to fix the ambiguities (one-two minutes) can be expected when only a subset of ambiguities is fixed instead of the complete vector (partial ambiguity resolution).

Ionospheric disturbances affect Global Positioning System (GPS) performance in terms of accuracy and integrity, especially over the equatorial region. During the period of the disturbances, GPS receivers suffer from a high noise level. Not taken into account by the current stochastic model, the ionospheric disturbances degrade GPS positioning accuracy. In addition, non-Gaussian tails are observed in the distribution of the noise during the period of the disturbances; therefore the integrity of GPS can also be affected. This paper develops a statistical solution that is able to mitigate effects of ionospheric disturbances on GPS accuracy and integrity using a commercial dual frequency receiver. The Rate of Total Electron Content (TEC) change Index (ROTI), a parameter derived from the dual frequency receiver, is used to group the levels of ionospheric disturbances. The standard deviations of the pseudorange noise under different groups are evaluated. By incorporating both the ROTI and the satellite elevation, a modified stochastic model is proposed to reduce the effect of the disturbed observation on the positioning accuracy. The performance of the model is evaluated by a test and an inflated sigma for each group is recommended for over-bounding anomalies of observations to protect the user against threats from ionospheric disturbances. This technique, together with results in this paper, can be applied to mitigate the effects of ionospheric disturbances on GPS.

Digital maps have a large potential to support safety-related Advanced Driver Assistance Systems (ADAS) by providing detailed road and environment information. However, one critical attribute – road accident hotspot – is not available from existing digital maps, and is also difficult to derive from practical surveying. This paper provides a Geographical Information Systems (GIS)-based approach for the production of digital hotspot maps, based on a historical accident dataset and geospatial methods in a GIS. In this approach, firstly the Kernel Density Estimation (KDE) method was used to identify hotspot distribution; secondly the Percent Volume Contour (PVC) method was coupled with KDE to extract hotspot patterns; and finally the map layers of hotspot patterns were integrated with classical navigation maps. Following a description for geospatial hotspot production, the derivation of hotspot property data is also discussed. In order to prove this approach, a small-area case study was carried out in the City Centre of Nottingham. The presented results demonstrate that this approach is useful and effective for solving the hotspot creation problem for ADAS, but other future works will be required to improve data effectiveness.

The observability of error states in Inertial Navigation System/Global Positioning System (INS/GPS) integration is of great importance. Rank tests or null space tests of the observability matrix have been adopted by previous works, however, for a time-varying system with a high-dimension error state vector, it is very difficult to analyse the observability matrix by these traditional methods. In this paper, the decoupled observability analysis method is proposed for an 18-dimensional INS/GPS integration system. By reducing the dimension of coupling error states, several six-dimensional decoupled observability sub-matrices are obtained, which make the observability analyses easier. The observability results of error states are obtained by the proposed method. Covariance simulation with an Extended Kalman filter (EKF) and a flying test were performed which confirmed the theoretical results.

On 27 December 2012 it was announced officially that the Chinese Navigation Satellite System BeiDou (BDS) was able to provide operational services over the Asia-Pacific region. The quality of BDS observations was confirmed as comparable with those of GPS, and relative positioning in static and kinematic modes were also demonstrated to be very promising. As Precise Point Positioning (PPP) technology is widely recognized as a method of precise positioning service, especially in real-time, in this contribution we concentrate on the PPP performance using BDS data only. BDS PPP in static, kinematic and simulated real-time kinematic mode is carried out for a regional network with six stations equipped with GPS- and BDS-capable receivers, using precise satellite orbits and clocks estimated from a global BDS tracking network. To validate the derived positions and trajectories, they are compared to the daily PPP solution using GPS data. The assessment confirms that the performance of BDS PPP is very comparable with GPS in terms of both convergence time and accuracy.

This paper focuses on the performance analysis of ionosphere monitoring using the measurements from a BeiDou Continuously Operating Reference Stations (CORS) network. Combined pseudo-range and carrier phase observations are used to estimate total electron content (TEC) and the hardware delay deviation is also computed. Using the observations from five BeiDou CORS in China, the TEC monitoring results were obtained from each station and compared with GPS monitoring results and also those from the Global Ionosphere Maps (GIM) model. Numerical computation shows that the BeiDou system has the ability to precisely detect the TEC diurnal variation trend on each station. The Residual Mean Square (RMS) difference between the BeiDou and the GIM model at a higher latitude station is about four TEC Units (TECU), while the RMS difference between the GPS and the GIM is about three TECU; at a lower latitude station this difference increases to six TECU for BeiDou and four TECU for the Global Positioning System (GPS); at the lowest latitude station in this study, the differences for both systems are about six TECU.

For mobile radars installed on a gyro-stabilised platform (GSP) that can steadily follow an East-North-Up (ENU) frame, attitude biases (ABs) of the platform and offset biases (OBs) of the radar are linear dependent variables. Therefore ABs and OBs are unobservable in the linearized registration equations; however, when combining them as new variables, the system becomes observable, and this model has been called the unified registration model (URM). Unlike GSP mobile radars, un-stabilised GSP (or UGSP) mobile radars are installed on the platform directly and rotate with the platform simultaneously. For UGSP, it is testified that both types of biases are independent and observable because the time-varying attitude angles (AAs)1 of the platform are included in the registration equations, which destroy the dependencies of both kinds of biases and lead us to propose a completely different linearized registration model– the All Augmented Model (AAM). AAM employs all OBs and ABs in the state vector and a Kalman filter (KF) to produce their estimates. Numerical simulation results show that the estimated performance of AAM is close to the Cramér-Rao lower bound (CRLB) and that the Root Mean Square Errors (RMSEs) of the rectified measurements by using AAM are more than 500 m smaller than by URM in all directions.

A loosely coupled Inertial Navigation System (INS) and Global Positioning System (GPS) are studied, particularly considering the constant lever arm effect. A five-element vector, comprising a craft's horizontal velocities in the navigation frame and its position in the earth-centred and earth-fixed frame, is observed by GPS, and in the presence of lever arm effect, the nonlinear observation equation from the state vector to the observation vector is established and addressed by the correction stage of an unscented Kalman filter (UKF). The conditionally linear substructure in the nonlinear observation equation is exploited, and a computationally efficient refinement of the UKF called marginalized UKF (MUKF) is investigated to incorporate this substructure where fewer sigma points are needed, and the computational expense is cut down while the high accuracy and good applicability of the UKF are retained. A performance comparison between UKF and MUKF demonstrates that the MUKF can achieve, if not better, at least a comparable performance to the UKF, but at a lower computational expense.

Geostationary Earth Orbit (GEO) satellites play a significant role in the space segment of the Chinese Area Navigation System. The C-Band transfer ranging method developed by the National Time Service Center (NTSC) has been widely used in the Chinese Area Positioning System (CAPS), with its advantages of separating satellite ranging from time synchronization and being unaffected by weather. The explicit ranging correction models for the C-Band transfer ranging method are introduced in detail in this article for the first time. Precise Orbit Determination (POD) using C-Band pseudo-range observation of GEO satellite 2010-001A in July 2012 has been conducted. The residual Root Mean Square (RMS) of each site and POD are analysed with orbit difference over overlaps of adjacent orbit arcs. Moreover, the orbit of the GEO satellite has been evaluated by Satellite Laser Ranging (SLR) data from both domestic and foreign SLR sites for the first time. The residual RMS of POD using C-Band observation is better than 0·1 m, and the orbit difference over overlaps of adjacent orbit arcs is better than 3 m. In addition, the residual RMS in line-of-sight for a SLR site in China are better than 1 m, while the RMS for the Yarragadee site in Australia is about 3·4 m. It has been shown that the GEO satellite orbit accords very well with the C-Band observation. Also, the distribution of CAPS stations affects the orbit precision. All sites in CAPS are now located in China with low and medium latitudes. The residual RMS of the SLR site in the southern hemisphere is larger than that of the site in China.

An approach formulated by vector algebra is proposed to deal with great circle sailing problems. Using the technique of the fixed coordinates system and relative longitude concept, derivations of formulae for this approach are simpler than those of the conventional methods. Due to fixing the initial great circle course, the great circle track (GCT) is determined. Since the course is fixed (known as “COFI” in this paper), the proposed approach, which we have named the “COFI method”, can directly calculate the waypoints along the GCT. It is considered that the COFI method is a more understandable and straightforward method to solve waypoint problems than older approaches in the literature. Based on the COFI method, a program has been developed for the navigator. In addition, the spherical triangle method with respect to the equator crossing point (STM-E) is developed by supplemental theorem. Several examples are demonstrated to validate the proposed COFI method and STM-E.

An Augmented Relative Navigation System (ARNS) is proposed for autonomous satellite formation flying in low-Earth-orbit (LEO). Inter-satellite ranging systems such as those based on radio frequency transmissions can provide additional observation information, e.g. inter-satellite distance measurement, which can be used to increase the Global Positioning System (GPS) stand-alone observation dimension, or treated as a non-linear equality constraint within a smoothly-constrained Kalman filter. Both approaches are implemented in the proposed ARNS described in this paper. An innovative phase integer ambiguity fixing and feedback scheme is implemented to increase the ambiguity fix rate of the GPS carrier phase measurements. A set of Gravity Recovery and Climate Experiment (GRACE) flight data is used to test and validate the relative navigation performance of the proposed methods. Results indicate that the augmented system can improve relative positioning accuracy by an order of magnitude.

In this note the Middle Latitude Rule is derived. Namely, to reach Great Circle vertex in two steps such that the total distance is a minimum, an initial rhumb line course equal to the orthodromic course at Middle latitude is to be used. The shortest distance is achieved if the rhumb line course is altered towards the vertex at the orthodrome-loxodrome intersection point.

In this paper, we present a high-precision Mars entry integrated navigation algorithm under large uncertainties via a desensitised extended Kalman filter (DEKF). Firstly, a new six degree-of-freedom Mars entry dynamics model is derived based on the angular velocity outputs of a gyro, which is free of modelling errors in the aerodynamic and control torques. Secondly, both the accelerometer outputs and radio measurements between orbiters and entry vehicle are used as the observations embedded in a navigation filter to perform state estimation and suppress the measurement noise. Finally, a desensitised extended Kalman filter, exhibiting the desirable property of efficiently reducing the sensitivity of state variables with respect to model and parameter uncertainties, is adopted in order to overcome the adverse effects of initial state errors and uncertainties during Mars atmospheric entry and further improve entry navigation accuracy. The numerical simulation results show that the DEKF-based integrated navigation algorithm developed in this paper can achieve a better navigation performance with higher accuracy when compared with the standard extended Kalman filter (EKF)-based integrated navigation algorithm in the presence of larger state errors and parameter uncertainties.

Many countries are making increased efforts to improve marine security and safety and develop ship surveillance techniques to satisfy the increasing demands. Space-borne Synthetic Aperture Radar (SAR) delivers high performance day/night all weather capabilities and a space-based Automatic Identification System (AIS) can give near real time and global coverage. Limited by the development of sensors and data processing techniques, the integration of space-borne SAR and AIS has much to offer ship surveillance. State-of-the-art data fusion methods have generally provided satisfactory performance. However, in high-density shipping or high sea-states, performance quality is less assured. This paper firstly investigates improved data association methods. The association methods based on the position feature are improved, and multi-feature-based association methods are proposed. Then, ship identification and tracking by the integration of space-borne SAR and AIS are researched further. Multi-source data fusion strategy is also investigated. Finally, the discussion is presented and the future works are emphasized in the conclusion.

Domain analysis has a well-documented history in peer reviewed academic literature; however there are few instances of its application to facilitate the assessment of system specific navigation risk. This paper details one example of a practical approach to domain analysis for a busy section of the River Thames in Central London. The results correlate well to known high risk collision areas on the river and help to quantify and corroborate expert opinion and local knowledge. However a number of conditions must be accounted for in undertaking a robust study such as the geography of the study site, the purpose and audience of the research, and the availability of data and its limitations.

Navigation and positioning system users are demanding greater accuracy and reliability in ever more challenging environments. This is driving a wave of rapid innovation, with the result that multisensor integrated navigation systems will become much more complex. This introduces a number of problems, including how to find the necessary expertise to integrate a diverse range of technologies, how to combine technologies from different organisations that wish to protect their intellectual property, and how to incorporate new navigation technologies and methods without having to redesign the whole system. It also makes it desirable to share development effort over a range of different applications. To address this, the feasibility of a modular approach to the design and development of multisensor integrated navigation and positioning systems is analysed. Assessments of the requirements of different user communities and the adaptability of the different navigation and positioning technologies to different contexts and requirements are presented. Based on this, the adoption of an open interface standard for modular integration is recommended and the issues to be resolved in developing that standard are outlined.

In this paper, a triangle matching algorithm using local gravity field maps is proposed to bound the drift errors inherent in Strapdown Inertial Navigation Systems (SINS) in gravity-aided navigation. This triangle matching algorithm has two main stages, the first is the initial matching stage, which has a coarse phase and a fine phase to address the large unknown initial errors made by INS, and the other is the tracking matching stage, which mainly aims at tracking the matching solution with the vehicle running in real time. Simulations were carried out using data for the Bohai Sea and South China Sea areas, to assess the effects of different initial errors on the matching solutions. Finally some experiments were carried out to evaluate the proposed algorithm. The results show that the triangle matching algorithm has some compelling advantages, such as a capability to address the large unknown initial errors made by INS, and good real-time quality of matching the gravity measurements with the local gravity maps.