A closed form of an algorithm to determine a Global Positioning System (GPS) satellite's position, velocity and acceleration is proposed, and an Earth Centred Earth Fixed (ECEF) to Earth Centred Inertial (ECI) transformation result using the Civil Navigation (CNAV) message is presented in this paper. To obtain the closed form of the GPS satellite velocity and acceleration determination algorithm using the CNAV, we analytically differentiated the IS-GPS-200F position determination function. The calculated data are transformed from the International Terrestrial Reference Frame (ITRF) to the Geocentric Celestial Reference Frame (GCRF) using an equinox-based transform algorithm that is defined in the IAU-2000 resolution system using the Earth Orientation Parameter (EOP) data. To verify the correctness of the proposed velocity and acceleration determination algorithm, the analytical results are compared to the numerical result. The equinox-based transformation result is compared to simple rotation about the z-axis, which does not use the EOP. The results show that by using the proposed algorithm and the equinox-based transformation together, the user can obtain more accurate navigation data in the ECI frame.

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.

For indoor pedestrian navigation with a shoe-mounted inertial measurement unit (IMU), the zero velocity update (ZUPT) technique is implemented to constrain the sensors' error. ZUPT uses the fact that a stance phase appears in each step at zero velocity to correct IMU errors periodically. This paper introduces three main contributions we have achieved based on ZUPT. Since correct stance phase detection is critical for the success of applying ZUPT, we have developed a new approach to detect the stance phase of different gait styles, including walking, running and stair climbing. As the extension of ZUPT, we have proposed a new concept called constant velocity update (CUPT) to correct IMU errors on a moving platform with constant velocity, such as elevators or escalators where ZUPT is infeasible. A closed-loop step-wise smoothing algorithm has also been developed to eliminate discontinuities in the trajectory caused by sharp corrections. Experimental results demonstrate the effectiveness of the proposed algorithms.

In view of the shortcomings of existing satellite navigation systems in deep-space performance, candidate architectures which utilise libration point orbits in the Earth-Moon system are proposed to create an autonomous satellite navigation system for lunar missions. Three candidate constellations are systematically studied in order to achieve continuous global coverage for lunar orbits: the Earth-Moon L1,2 two-satellite constellation, the Earth-Moon L2,4,5 three-satellite constellation and the Earth-Moon L1,2,4,5 four-satellite constellation. After a thorough search for possible configurations, the latter two constellations are found to be the simplest feasible architectures for lunar navigation. Finally, an autonomous orbit determination simulation is performed to verify the autonomy of the system and two optimal configurations are obtained in a comprehensive consideration of coverage and autonomous orbit determination performance.

This paper looks at the navigational challenges faced by William Dampier when, as Captain of the Royal Navy ship Roebuck, in 1699, he approached, and then found his way along the coast of Western Australia (at that time known as New Holland). A discussion of the methods and instruments available to Dampier is followed by consideration of how, and with what success, he went about his task. Dampier's own account of the voyage was included in his book A Voyage to New Holland (Dampier, 1703) although this is likely to have been heavily edited, and perhaps even rewritten by a “man of letters” to make it more attractive to the general public. For this reason and, bearing in mind that autobiographical work may contain omissions or otherwise be slanted to show the writer in his best light, the navigational information in his book has been cross-checked with the Roebuck's original Master's Log, held by the UK National Archives at Kew (Documents ADM 52/94). Jacob Hughes was the ship's Master, but the Log entries were written in at least two hands.

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.

Outliers in terrain data are an obstacle to achieving accurate and robust solutions of Underwater Terrain Relative Navigation (UTRN). If not handled properly, navigation may be degraded or even divergent. To address the problem, this paper proposes a terrain-matching algorithm based on the robust estimation theory. In contrast to the conventional approach, the proposed algorithm can significantly reduce the interference of the outliers. Experimental results confirm the good performance of the proposed method.

This paper proposes a precise and fast direction of arrival estimation method using Global Navigation Satellite System (GNSS) carrier phase measurements. Single-epoch, single-satellite integer cycle ambiguities are reliably resolved by making use of constraints and taking advantages of antenna arrays. The algorithm shows good robustness in cases where signal interruption or corruption occurs on some antenna elements as long as four antenna elements in a non-planar array have uncorrupted observables. The algorithm is demonstrated by field tests where antenna elements are connected to multiple receivers with an external common clock. The results indicate a high success rate of single-epoch ambiguity resolution and high direction of arrival accuracy.

This paper addresses the issue of state estimation in the integration of a Strapdown Inertial Navigation System (SINS) and Global Positioning System (GPS), which is used for airborne earth observation positioning and orientation. For a nonlinear system, especially with large initial attitude errors, the performance of linear estimation approaches will degrade. In this paper a nonlinear error model based on angle errors is built, and a nonlinear estimation algorithm called the Central Difference Rauch-Tung-Striebel (R-T-S) Smoother (CDRTSS) is utilized in SINS/GPS integration post-processing. In this algorithm, the measurements are first processed by the forward Central Difference Kalman filter (CDKF) and then a separate backward smoothing pass is used to obtain the improved solution. The performance of this algorithm is compared with a similar smoother based on an extended Kalman filter known as ERTSS through Monte Carlo simulations and flight tests with a loaded SINS/GPS integrated system. Furthermore, a digital camera was used to verify the precision of practical applications in a check field with numerous reference points. All these validity checks demonstrate that CDRTSS is a better method and the work of this paper will offer a new approach for SINS/GPS integration for Synthetic Aperture Radar (SAR) and other airborne earth observation tasks.

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.

A large interest in developing commercial Location-Based Services (LBS) and the necessity of implementing emergency call services, have led to the intensive development of techniques for mobile users' localisation. In this paper, a Public Land Mobile Networks (PLMN) -based technique for initial position determination is proposed as an alternative to satellite-based methods in environments with obstructed satellite signals. Two positioning models, based on handset available Received Signal Strength (RSS) measurements from Global System for Mobile Communications (GSM) base stations and the use of Support Vector Machine (SVM) algorithms, are proposed. Performances of proposed models are verified using field measurements, collected in a suburban environment. Models are analysed in terms of positioning accuracy, complexity and latency, and compared to some other promising PLMN-based techniques. Using proposed SVM-based positioning models a median error of 4·3 m–6·2 m and latency of less than a second can be achieved.

The advent of multiple Global Navigation Satellite System (GNSS) constellations will result in a considerable increase in the number of satellites for positioning worldwide. This substantial improvement in measurement redundancy has the potential to radically advance receiver autonomous integrity monitoring (RAIM) performance. However, regardless of the number of satellites, the performance of existing RAIM methods is sensitive to the assumed prior probabilities of individual fault hypotheses. In this paper, a new method is developed using Bayes’ theorem to generate upper bounds on posterior probabilities of individual fault hypotheses given current user measurements. These bounds are used in a Bayesian fault-tolerant position estimator (FTE) that minimizes integrity risk. The detection test statistic is a measurement-based integrity risk bound, which is directly compared with a pre-specified risk requirement. The associated challenge of quantifying continuity risk is resolved using a bounding approach, which is also detailed in this work. The new Bayesian FTE method is shown to be more robust to uncertainty in prior probability of fault occurrence than existing RAIM methods.

Multipath propagation can cause significant impairments to the performance of Global Navigation Satellite System (GNSS) receivers and is often the dominant source of accuracy degradation for high precision GNSS applications. Commonly used time-of-arrival estimation techniques cannot provide the required estimation accuracy in severely dense multipath environments such as urban canyons. Multipath components are highly correlated and this results in a rank deficiency of the signal autocorrelation matrix. In this paper the Doppler spectrum broadening of the fast fading channel resulting from the motion of the receiver or surrounding objects is employed to decorrelate signal reflections for the purpose of high-resolution estimation of multipath delays through the subspace-based Multiple Signal Classification (MUSIC) technique. Specifically, delay-domain correlator outputs at different Doppler frequencies are combined to enhance the rank of the signal autocorrelation matrix. Simulation and results of real data collected in an urban environment (downtown Calgary) are presented to compare the performance of the proposed method with the spatial-temporal-diversity-based MUSIC technique and a widely available algorithm in commercial GNSS receivers, namely the double-delta correlator technique. The performance metrics are based upon pseudorange and positioning errors, which are derived using an accurate reference trajectory established using a high precision GNSS-INS integrated system.

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).

To eliminate the impact of the Doppler effects caused by the motion of the Mars explorer, a novel X-ray pulsar navigation method based on a closed-loop filter is proposed. In the pulsar signal observation period, the Doppler velocity predicted by the orbit dynamic model and the prior information is utilised to compensate the X-ray photon time-of-arrival (TOA). However, because of the error in prior information, there is a bias caused by the Doppler compensation in the pulse time-of-arrival. The pulse TOA bias and the Mars explorer's state estimation error are correlated, which results in the decline of the Kalman filter performance. To deal with this problem, we build the TOA measurement model with respect to the state estimation error, and utilise the closed-loop extended Kalman filter (EKF) as the navigation filter, where the predicted state error is adopted as the state estimation. The simulation results demonstrate the feasibility, real-timeliness and effectiveness of the proposed navigation method. The navigation method based on the closed-loop EKF using the measurement model with the Doppler effects is more accurate than the traditional one.

The integration of Global Positioning Systems (GPS) with Inertial Navigation Systems (INS) has been very actively studied and widely applied for many years. Some sensors and artificial intelligence methods have been applied to handle GPS outages in GPS/INS integrated navigation. However, the integrated system using the above method still results in seriously degraded navigation solutions over long GPS outages. To deal with the problem, this paper presents a GPS/INS/odometer integrated system using a fuzzy neural network (FNN) for land vehicle navigation applications. Provided that the measurement type of GPS and odometer is the same, the topology of a FNN used in a GPS/INS/odometer integrated system is constructed. The information from GPS, odometer and IMU is input into a FNN system for network training during signal availability, while the FNN model receives the observations from IMU and odometer to generate odometer velocity correction to enhance resolution accuracy over long GPS outages. An actual experiment was performed to validate the new algorithm. The results indicate that the proposed method can improve the position, velocity and attitude accuracy of the integrated system, especially the position parameters, over long GPS outages.

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.

COMPASS or BeiDou is the new satellite navigation system under construction in China. In this paper, the standalone performance of COMPASS is compared to the Global Positioning System (GPS), including: Single Point Positioning (SPP), differential positioning (DGPS and Differential COMPASS) and single epoch ambiguity resolution and positioning. Based on the results, it was found that COMPASS SPP performance is clearly worse than that of GPS, due to larger broadcast orbit and satellite clock errors, especially the latter. Differential positioning performance of COMPASS and GPS are essentially similar, with GPS marginally better. COMPASS single epoch ambiguity resolution performance is obviously better than that of GPS due to more observed satellites and the single epoch positioning performance of COMPASS and GPS are similar.

Integer ambiguity resolution is able to improve positioning accuracy and reduce convergence time in Precise Point Positioning (PPP). Although significantly improved horizontal positioning accuracy has been demonstrated, the height solution improvement is found to be less significant, and improving this requires further investigation. In this paper, a troposphere constraint method using precise troposphere corrections is proposed to improve the PPP ambiguity-resolved height solution. This is different from the conventional approach that typically applies meteorological data to calculate the a priori troposphere delay and estimates the residual troposphere delay. The effects of the troposphere delay on PPP ambiguity-resolved height solutions are first studied. Numerical analysis is conducted to ambiguity-resolved positioning results based on the decoupled clock model and hourly Global Positioning System (GPS) observations from a Canadian PPP-inferred troposphere precipitable water vapour system. The results show that by using the proposed method the PPP ambiguity-resolved height accuracy can be further improved to 3·86 cm compared to 5·32 cm using the conventional approach.

Gaussian process regression (GPR) is used in a Spare-grid Quadrature Kalman filter (SGQKF) for Strap-down Inertial Navigation System (SINS)/odometer integrated navigation to bridge uncertain observation outages and maintain an estimate of the evolving SINS biases. The SGQKF uses nonlinearized dynamic models with complex stochastic nonlinearities so the performance degrades significantly during observation outages owing to the uncertainties and noise. The GPR calculates the residual output after factoring in the contributions of the parametric model that is used as a nonlinear SINS error predictor integrated into the SGQKF. The sensor measurements and SINS output deviations from the odometer are collected in a data set during observation availability. The GPR is then applied to predict SINS deviations from the odometer and then the predicted SINS deviations are fed to the SGQKF as an actual update to estimate all SINS biases during observation outages. We demonstrate our method's effectiveness in bridging uncertain observation outages in simulations and in real road tests. The results agree with the theoretical analysis, which demonstrate that SGQKF using GPR can maintain an estimate of the evolving SINS biases during signal outages.