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.

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.

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).

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.

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.

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.

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.

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.

Navigational software often lacks official standardisation of the methods used and their accuracy due to commercial confidentiality. The “black box solutions” used by navigational systems are unknown, thus a logical and simple method to solve navigational problems must be presented. This paper presents new meridian arc formulae by the least squares method. As the traditional meridian arc formulae cannot be expressed as a closed form, they are often truncated to the first few terms for practical use and in doing so neglect the values not used. By forming an overdetermined system with known components of the traditional meridian arc formula and actual length of the meridian arc, the least squares method can be used to approximate the best fitting coefficients for the traditional meridian arc formulae and forms the new compact formulae. The new formulae are based on highly accurate values of the meridian arc for the WGS-84 ellipsoid datum, and are perfect for the computational algorithms implemented in navigational software such as Geographic Information Systems (GIS), Electronic Chart Display and Information Systems (ECDIS) and other Electronic Chart Systems (ECS). Their accuracy is compared with other methods and shows that the new proposed formulae are shorter and accurate with negligible errors. The new formulae can be adapted to the accuracy needed and imply different numbers of coefficients. This can also shorten the calculations in navigation such as rhumb-line or great elliptic sailing on the ellipsoid because the meridian arc length is essential for these calculations.

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.

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.

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.