The authors give a personal account of the use of astro navigation during the years before GPS became the primary aid for oceanic navigation. The paper also contains an account of the support provided by The Nautical Almanac (NA) together with its associated tables and computer programs which ease the tedium of sight reduction while leaving the satisfaction to be found in successful astro observations at sea.

An early version of Section 2 of this paper formed part of a presentation made at the Symposium After Longitude – Modern Navigation in Context which took place at the UK National Maritime Museum from 22–23 March 2012.

Europe and the USA are developing plans (‘SESAR’ and ‘NextGen’) to transform the processes of Air Traffic Management (ATM). These will improve safety and efficiency, and match predicted increases in air transportation demand. Aircraft would fly on Four Dimensional-Trajectories (4D-Trajectories), incorporating altitude, position, time, and other aircraft positions and vectors. This vision would involve extremely large investments from the airline industry and ATM service providers. Thus, development priorities need to be based on sound business cases. But will these necessarily lead to the strategic vision of a 4D-Trajectory system? Will the changes in practice be limited to a series of short and medium term operational improvements rather than strategic improvements? Killer App(lication)s is jargon for innovations so valuable that they prove the core value of some larger technology. So, are there ‘Killer Apps’ for 4D-Trajectory ATM? Killer Apps generate high degrees of stakeholder technical and financial cooperation. Ironically, most past ATM Killer Apps have improved safety. The analysis here attempts to identify and then size potential 4D-Trajectory ATM Killer Apps. The evidence for Killer Apps has to pass key tests. Killer Apps obviously have to offer enormous benefits to stakeholders in the context of the potential costs. The bulk of these benefits must not be obtainable through technologically ‘cut down’ non−4D-Trajectory versions. Part 1 of this paper sets out the framework for investigating these questions; Part 2 will be published subsequently and will examine potential Killer Apps derived from improvements in Fuel Efficiency, Capacity and Cost. An abbreviated version of this paper was first presented at the European Navigation Conference (ENC 2011), London in November 2011.

This paper proposes a new method for estimating Automatic Identification System (AIS) coverage empirically from received transmissions. The method is appropriate for stationary coverage assets, as distinct from aircraft and satellites. The key idea behind the method is to interpolate probabilistically between AIS reports in order to reconstruct where the missed transmissions might have occurred. These hypothetical missed transmissions then supplement the received ones in a coverage estimate based on a Bayesian treatment of a binomial model of reception. The final estimate of the coverage is implemented over a spatial grid. The method is demonstrated on simulated AIS data and was found to have lower mean squared error than a previously published method. Assumptions and potential weaknesses of the new method are discussed.

This paper presents an approach for outdoor navigation of an autonomously guided canine using an embedded command module with vibration and tone generation capabilities and an embedded control suite comprised of a microprocessor, wireless radio, GPS receiver, and an Attitude and Heading Reference System. In order to determine the canine's motions, which inherently contain non-conventional noise characteristics, the sensor measurements were integrated using a specialized Extended Kalman Filter (EKF), equipped with a Fuzzy Logic controller for adaptive tuning of the Process Noise Covariance Matrix. This allowed for rejection of un-modelled canine motion characteristics which tend to corrupt accelerometer bias tracking in a standard EKF. The EKF solution provided an optimized estimate of the canine position and velocity and also proved to be effective in tracking the canine's position (within 7·5 m) and velocity (within 1·2 m/s) during simulated 10 second GPS outages.

Global Positioning System (GPS) has been used as a primary source of navigation in land and airborne applications. However, challenging environments cause GPS signal blockage or degradation, and prevent reliable and seamless positioning and navigation using GPS only. Therefore, multi-sensor based navigation systems have been developed to overcome the limitations of GPS by adding some forms of augmentation. The next step towards assured robust navigation is to combine information from multiple ground-users, to further improve the chance of obtaining reliable navigation and positioning information. Collaborative (or cooperative) navigation can improve the individual navigation solution in terms of both accuracy and coverage, and may reduce the system's design cost, as equipping all users with high performance multi-sensor positioning systems is not cost effective. Generally, ‘Collaborative Navigation’ uses inter-nodal range measurements between platforms (users) to strengthen the navigation solution. In the collaborative navigation approach, the inter-nodal distance vectors from the known or more accurate positions to the unknown locations can be established. Therefore, the collaborative navigation technique has the advantage in that errors at the user's position can be compensated by other known (or more accurate) positions of other platforms, and may result in the improvement of the navigation solutions for the entire group of users. In this paper, three statistical network-based collaborative navigation algorithms, the Restricted Least-Squares Solution (RLESS), the Stochastic Constrained Least-Squares Solution (SCLESS) and the Best Linear Minimum Partial Bias Estimation (BLIMPBE) are proposed and compared to the Kalman filter. The proposed statistical collaborative navigation algorithms for network solution show better performance than the Kalman filter.

Positioning using the Global Positioning System (GPS) is unreliable in dense urban areas with tall buildings and/or narrow streets, known as ‘urban canyons’. This is because the buildings block, reflect or diffract the signals from many of the satellites. This paper investigates the use of 3-Dimensional (3-D) building models to predict satellite visibility. To predict Global Navigation Satellite System (GNSS) performance using 3-D building models, a simulation has been developed. A few optimized methods to improve the efficiency of the simulation for real-time purposes were implemented. Diffraction effects of satellite signals were considered to improve accuracy. The simulation is validated using real-world GPS and GLObal NAvigation Satellite System (GLONASS) observations.

The performance of current and future GNSS in urban canyons is then assessed by simulation using an architectural city model of London with decimetre-level accuracy. GNSS availability, integrity and precision is evaluated over pedestrian and vehicle routes within city canyons using different combinations of GNSS constellations. The results show that using GPS and GLONASS together cannot guarantee 24-hour reliable positioning in urban canyons. However, with the addition of Galileo and Compass, currently under construction, reliable GNSS performance can be obtained at most, but not all, of the locations in the test scenarios. The modelling also demonstrates that GNSS availability is poorer for pedestrians than for vehicles and verifies that cross-street positioning errors are typically larger than along-street due to the geometrical constraints imposed by the buildings. For many applications, this modelling technique could also be used to predict the best route through a city at a given time, or the best time to perform GNSS positioning at a given location.

Global Navigation Satellite Systems (GNSS) Doppler measurements are commonly used for velocity-based relative positioning and aiding Inertial Navigation Systems (INS) in signal degraded environments. The aim of this paper is to characterise the Doppler measurements in GNSS harsh multipath environments. In multipath fading situations such as indoor and urban canyon environments, multipath components arrive to the receiver antenna from different paths and directions. These give rise to various Doppler shifts that cause errors in the velocity solution. In this work the Doppler measurements discrepancy characterised by Doppler spread in multipath environments is investigated. By assuming a ‘sphere of scatterers’ model and considering the antenna gain pattern, the theoretical Power Spectral Density (PSD) observed by a receiver is formulated. The theoretical findings are examined using two sets of measurements in dense multipath environments. Global Positioning System (GPS) live signals using non-isotropic antennas with different orientations are used for this purpose. Different motion directions are also examined using different data sets. An Assisted GPS (A-GPS) approach is utilised where the code phase and the navigation data bits are provided by a nearby outdoor antenna. By applying a ‘Block Processing’ technique, an epoch-by-epoch Doppler and velocity estimation is implemented. Herein, the Doppler and velocity measurements accuracy in addition to the Doppler spread characterization are studied. As shown both theoretically and experimentally, in harsh multipath environments the PSD of the observed signals is a function of the scatterers' geometry and the antenna gain pattern. The Doppler estimation accuracies in multipath and multipath-free cases are compared for different ranges of Carrier-to-Noise ratio (C/N0). Theoretical and experimental results revealed inaccurate Doppler estimation and poor Doppler-derived velocity solutions in dense multipath environments.

The fusion of multi-sensor data can provide more accurate and reliable navigation performance than single-sensor methods. However, the general Federated Kalman Filter (FKF) is not suitable for large changes of complex nonlinear systems parameters and is not optimized for effective information sharing coefficients to estimate navigation preferences. This study concerns research on the FKF method for a nonlinear adaptive model based on an improved Genetic Algorithm (GA) for the Strapdown Inertial Navigation System (SINS) / Celestial Navigation System (CNS) / Global Positioning System (GPS) integrated multi-sensor navigation system. An improved fitness function avoids the premature convergence problem of a general GA and decimal coding improves its performance. The improved GA is used to build the adaptive FKF model and to select the optimized information sharing coefficients of the FKF. An Unscented Kalman Filter (UKF) is used to deal with the nonlinearity of integrated navigation system. Finally, a solution and implementation of the system is proposed and verified experimentally.

Integer ambiguity resolution in Precise Point Positioning (PPP) can shorten convergence time and improve accuracy significantly. Uncalibrated Fractional Offsets (UFOs) originating in the satellites destroy the integer nature of carrier phase ambiguities observed at a single station. Several methods have been developed to estimate UFO information from a reference network for PPP ambiguity resolution. In this paper, we present a new approach for estimating Zero-Differenced (ZD) UFOs via float ZD ambiguities from a reference network. In this new approach, UFOs for receivers and satellites are estimated in an integrated adjustment with integer ambiguities being resolved sequentially, so that UFOs of higher quality can be achieved. The float ZD ambiguities used in the estimation can be from network or PPP solutions. Using those from PPP solutions enables the time-consuming clock estimations and the UFO estimations to be carried out separately, so that UFOs can be estimated more reliably from a much denser network. In this paper, a data processing procedure, from the estimation of UFOs through to PPP ambiguity fixing, is designed and proposed. The approach is validated with several data sets in various scenarios. The results show that satellite UFOs can be estimated precisely and reliably by using the observations from a reference network, in which the station spacing could be up to thousands of kilometres. With 30 minutes of observations, a PPP solution with fixed integer ambiguities is achievable and the positioning accuracy can be improved significantly when compared with its float solution.

Gravity Assist (GA) is a kind of transfer orbit technology widely used in interplanetary missions, which highly depends on navigation performance to succeed. The Orbital Dynamic Equation is an essential component in the navigation system, affected by factors including the numerical integrator, perturbing planets, integration step size, gravitational constant and planet ephemerides. To analyse the impact factors mentioned above and investigate an efficient system model, the propagation and navigation results are carried out in a Mars-assist explorer scenario; a specific case study is also provided in this paper. The results indicate that the planetary ephemeris uncertainty and integration size are the dominant error sources, and the integration step size is the dominant impact factor on the real-time performance. In this specific case, the ‘Orbital Dynamic Equation’ considering Sun and Mars perturbation is suggested for integration by RK4 with 60 s integration step size. The conclusions drawn by this study are particularly useful in the design, construction, and analysis of an autonomous navigation system for a GA explorer.

In this paper, equations are established to solve problems of Rhumb Line Sailing (RLS) on an oblate spheroid. Solutions are provided for both the inverse problem and the direct problem, thereby providing a complete solution to RLS. Development of these solutions was achieved in part by means of computer based symbolic algebra. The inverse solution described attains a high degree of accuracy for distance and azimuth. The direct solution has been obtained from a solution for latitude in terms of distance derived with the introduction of an inverse series expansion of meridian arc-length via the rectifying latitude. Also, a series to determine latitude at any longitude has been derived via the conformal latitude. This was achieved through application of Hermite's Interpolation Scheme or the Lagrange Inversion Theorem. Numerical examples show that the algorithms are very accurate and that the differences between original data and recovered data after applying the inverse or direct solution of RLS to recover the data calculated by the direct or inverse solution are very small. It reveals that the algorithms provided here are suitable for programming implementation and can be applied in the areas of maritime routing and cartographical computation in Graphical Information System (GIS) and Electronic Chart Display and Information System (ECDIS) environments.

GNSS relative positioning technique is an important field of study, in which the standard ‘GNSS Baseline Model’ is often used. Differencing between observation equations is used to construct the mathematical model, since this method can eliminate some common errors in the GNSS signal measurements. The ‘Orthogonal Transformation’ method can also construct the GNSS Baseline Model. However, as is described by some scholars, this model may avoid some drawbacks of Double Differencing (DD) while maintaining all the advantages. For comparison purposes, this model is evaluated and the theoretical equivalence of both approaches is proved for the short baseline from two aspects: the Integer Ambiguity Resolution and the conditional least-squares baseline vector.