In the middle years of the 20th Century, few merchant ships were fitted with radar and, on those that were, shipmasters often looked upon it as a distraction from a watchkeeper's proper duties rather than as a useful aid to navigation.

For shipmasters of that persuasion, the only place to keep watch was outside the wheelhouse on an exposed bridge wing; mostly the starboard wing because the COLREGS (‘Collision Regulations’ or, more properly, ‘The International Regulations for Preventing Collisions at Sea’) required us to give way to ships approaching from the starboard side. Well, the bridge wing was an attractive place to spend a few hours on a calm, tropical night, but it could be highly disagreeable and sometimes, I thought, actually dangerous, in a North Atlantic rainstorm.

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.

This paper charts the history of Global Satellite Navigation Systems (GNSS) from the earliest days of the ‘Space Race’ in the 1960s and 1970s to the latest plans for modernisation of existing systems and the development of new systems yet to be deployed or become operational. The paper is based on lectures and presentations given by the author to postgraduate students at The University of Nottingham, students on the RAF General Duties Aero-Systems Course at the Air Warfare Centre, RAF Cranwell and to a number of RIN, RAeS and IEE Branches and to local aviation groups.

The USA and Europe are developing plans – NextGen and SESAR – to transform the processes of Air Traffic Management (ATM). These will improve safety and efficiency, and match predicted increases in air transportation demand. They use advanced networking technology updated with information from satellite navigation and digital non-voice communication. The strategic goal, envisaged for 15–20 years hence, is a new ATM paradigm. Aircraft would fly on Four-Dimensional (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? So, are there ‘Killer Apps’ for 4D-trajectory ATM? ‘Killer App(lication)s’ is jargon for innovations so valuable that they prove the core value of some larger technology. Killer Apps generate high degrees of stakeholder technical and financial cooperation. Ironically, most past ATM Killer Apps have improved safety, e.g., modern radar data processing led to collision avoidance systems. 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 (Brooker, 2012a) sets out the framework for investigating these questions. Part 2 examines 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.

Shoe mounted Inertial Measurement Units (IMU) are often used for indoor pedestrian navigation systems. The presence of a zero velocity condition during the stance phase enables Zero Velocity Updates (ZUPT) to be applied regularly every time the user takes a step. Most of the velocity and attitude errors can be estimated using ZUPTs. However, good heading estimation for such a system remains a challenge. This is due to the poor observability of heading error for a low cost Micro-Electro-Mechanical (MEMS) IMU, even with the use of ZUPTs in a Kalman filter. In this paper, the same approach is adopted where a MEMS IMU is mounted on a shoe, but with additional constraints applied. The three constraints proposed herein are used to generate measurement updates for a Kalman filter, known as ‘Heading Update’, ‘Zero Integrated Heading Rate Update’ and ‘Height Update’.

The first constraint involves restricting heading drift in a typical building where the user is walking. Due to the fact that typical buildings are rectangular in shape, an assumption is made that most walking in this environment is constrained to only follow one of the four main headings of the building. A second constraint is further used to restrict heading drift during a non-walking situation. This is carried out because the first constraint cannot be applied when the user is stationary. Finally, the third constraint is applied to limit the error growth in height. An assumption is made that the height changes in indoor buildings are only caused when the user walks up and down a staircase. Several trials were shown to demonstrate the effectiveness of integrating these constraints for indoor pedestrian navigation. The results show that an average return position error of 4·62 meters is obtained for an average distance of 1557 meters using only a low cost MEMS IMU.

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 aims to estimate Vessel Collision Frequency in the Singapore Strait. This frequency is obtained as the product of the number of Vessel Conflicts and the causation probability using the real-time vessel movement data from the Lloyd's Marine Intelligence Unit (Lloyd's MIU) database. The results show that the container carriers have the highest Vessel Collision Frequency while Roll-On Roll-Off (RORO) and passenger ships have the lowest frequency. Tankers cause the highest head-on collision frequency. In the Singapore Strait, the most risky overtaking area is between longitudes 103°48′E and 104°12′E. The most risky head-on area is between longitudes 103°50′E and 104°00′E while the majority of crossing collisions occur between longitudes 103°50′E and 104°12′E. The Vessel Collision Frequency is found to be 1·75 per year in the traffic lanes. Currently, westbound traffic in the Strait is more risky than eastbound traffic (the number of westbound collisions in July was 0·0991 while the number of eastbound collisions was 0·0470). Furthermore, the estimated Vessel Collision Frequency during the day is less than that at night. The results of this paper could be beneficial for the Maritime and Port Authority of Singapore to further enhance the navigational safety strategies implemented in the Singapore Strait.

The aim of this research was to clarify and quantify the demands of the working environment and watch-keeping regime for large commercial ships in relation to dark adaptation. The night lookout task requires the identification of the relatively bright navigational lights of other ships against the dark background of the sky and sea. The probability of detection is determined by the ambient lighting conditions on the bridge and the dark adapted state of vision. Light levels were such that threshold sensitivity (after 15 minutes) was reduced by around 2 log units in comparison to complete darkness. This has implications for the effective range of navigational lights at sea as defined in regulations. The intensity and position of navigation lights on larger vessels is such that the sensitivity of the eye under typical bridge conditions is likely to be sufficient for their visibility to be acceptable. This may not be the case for less well lit small craft.

Galileo is a global civil navigation satellite system developed in Europe as an alternative to the GPS controlled by the US Department of Defense and GLONASS controlled by Russian Space Forces. It is scheduled to be operative in 2013 and it will have 30 satellites orbiting on three inclined planes with respect to the equatorial plane at an altitude of about 24 000 km. The aim of this work is the study of the pseudorange error of the GIOVE satellites. To achieve this goal, the specifications defined in Giove A-B Navigation Signal in Space Interface Control Document (ICD) are used to develop a suitable software tool in MATLAB® environment. The tool is able to compute GIOVE A and GIOVE B position from the broadcast ephemerides, to calculate the pseudorange error and to process it. From the known receiver position and the computed satellite coordinates, the geometric range is obtained and compared with the pseudorange measurement, in order to obtain the pseudorange error.

Terrain Referenced Navigation (TRN) is based on the comparison of terrain altitude measurements with a reference map. Similar to code acquisition and tracking in Global Positioning System (GPS), the TRN system needs to find and track a particular sequence of measurements in a larger dataset. In our earlier work, these correspondences have been exploited to design a GPS inspired algorithm for TRN. The tracking loop is implemented as an early-late correlator, based on the DLL functional principle. Differences between GPS and terrain data in terms of signal properties are often based on the analysis of an ‘ideal’ GPS signal. In reality a GPS signal suffers from disturbances such as multipath and interference. This paper focuses on the identification and evaluation of potential GPS multipath mitigation strategies to be used to partly mitigate the issues caused by the non-ideal terrain signal. Results for the TRN implementations are described in a comparative manner. The content of this paper was presented during the European Navigation Conference 2011 in London.

Vehicular communication technologies are becoming staples of modern societies. This paper proposes a new positioning algorithm for vehicular networks. The algorithm is a non-classic Multi-Dimensional Scaling Filter (MDSF) that builds on a novel and computationally effective Multi-Dimensional Scaling (MDS) solution covariance estimation technique and also a Maximum Likelihood (ML) filter. In general a major drawback of the non-classic MDS is the high computational cost because of its iterative nature. It is shown that a special blend between vehicular Map-Matching (MM) and MDSF considerably reduces the number of iterations and the convergence time, making the MDSF a suitable algorithm for vehicular network positioning. The performance of MDSF is compared with that of an Extended Kalman Filter (EKF) together with the Cramar Rao Lower Bound (CRLB). It is shown through simulation that for all types of traffic conditions MDSF performs better than EKF and closer to CRLB than EKF. It is also shown that both MDSF and EKF algorithms are robust to typical Global Positioning System (GPS) outages in deep urban canyons. CRLB also proves that Cooperative Positioning (CP) in general has the ability to bridge short GPS outages.

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.

The determination of the correct integer number of carrier cycles (integer ambiguity) is the key to high accuracy positioning with carrier phase measurements from Global Navigation Satellite Systems (GNSS). There are a number of current methods for resolving ambiguities including the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method, which is a combination of least-squares and a transformation to reduce the search space. The current techniques to determine the level of confidence (integrity) of the resolved ambiguities (i.e. ambiguity validation), usually involve the construction of test statistics, characterisation of their distribution and definition of thresholds. Example tests applied include ratio, F-distribution, t-distribution and Chi-square distribution. However, the assumptions that underpin these tests have weaknesses. These include the application of a fixed threshold for all scenarios, and therefore, not always able to provide an acceptable integrity level in the computed ambiguities. A relatively recent technique referred to as Integer Aperture (IA) based on the ratio test with a large number of simulated samples of float ambiguities requires significant computational resources. This precludes the application of IA in real time.

This paper proposes and demonstrates the power of an integrity monitoring technique that is applied at the ambiguity resolution and positioning stages. The technique has the important benefit of facilitating early detection of any potential threat to the position solution, originating in the ambiguity space, while at the same time giving overall protection in the position domain based on the required navigation performance. The proposed method uses the conventional test statistic for ratio testing together with a doubly non-central F distribution to compute the level of confidence (integrity) of the ambiguities. Specifically, this is determined as a function of geometry and the ambiguity residuals from least squares based ambiguity resolution algorithms including LAMBDA. A numerical method is implemented to compute the level of confidence in real time.

The results for Precise Point Positioning (PPP) with simulated and real data demonstrate the power and efficiency of the proposed method in monitoring both the integrity of the ambiguity computation and position solution processes. Furthermore, due to the fact that the method only requires information from least squares based ambiguity resolution algorithms, it is easily transferable to conventional Real Time Kinematic (RTK) positioning.

Today's mobile technology features several sensors that when integrated can provide ubiquitous navigation assistance to pedestrians including wheelchair users. Common sensors found in most smartphones are Global Positioning System (GPS), accelerometer, and compass. In this paper, a user's movement pattern recognition algorithm to improve map matching efficiency and accuracy in pedestrian/wheelchair navigation systems/services is discussed. The algorithm integrates GPS positions, orientation data from compass, and movement states recognized from accelerometer data in a client/server architecture. The algorithm is tested in an Android mobile phone, and the results show that the proposed map matching algorithm is efficient and provides good accuracy.

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.

In this paper, a Three Dimensional Pedestrian Movement Model (3D-MM) capable of probabilistically representing pedestrian movement in challenging indoor and outdoor localization environments is developed, implemented and evaluated. In the scope of this paper, the model is used to generate a ‘movement’ or a transition for dynamic positioning systems that are based on sequential Bayesian filtering techniques, such as particle filtering. It can also be used to assign weights for particles' movements proposed by sensors in Likelihood Particle Filters implementations. Alternatively, the developed model can be applied to other applications domains such as infrastructure design, evacuation planning, robot-human interaction and pervasive computing. The novelty of the model is in its ability to characterize both random and goals-oriented pedestrian motions and additionally use the a priori knowledge of maps and floor plans. It will be shown that an appropriate pedestrian movement model not only improves the positioning accuracy, but is also essential for a robust positioning estimator. Additionally, this work shows that maps and floor plans can improve pedestrian movement models but do not replace them, as several authors suggest.

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.

The basic idea of a dead reckoning personal navigator is to integrate incremental motion information in the forms of step length and step direction over time. Considering that the displacement components are estimated for each step-cycle, it is essential to monitor the integrity of these parameters; otherwise, the error accumulation may render the system unstable. In this paper, a two-stage Kalman Filter (KF) augmented by a neural network is developed to facilitate integrity monitoring. The preliminary results, obtained from several tests performed on simulated and real-word data, indicate an 80% success rate in integrity monitoring.

Recent developments in GPS positioning show that a user with a standalone GPS receiver can obtain positioning accuracy comparable to that of carrier-phase-based differential positioning. Such technique is commonly known as Precise Point Positioning (PPP). A significant challenge of PPP, however, is that about 30 minutes or more is required to achieve centimetre to decimetre-level accuracy. This relatively long convergence time is a result of the un-modelled GPS residual errors. A major residual error component, which affects the convergence of PPP solution, is higher-order Ionospheric Delay (IONO). In this paper, we rigorously model the second-order IONO, which represents the bulk of higher-order IONO, for PPP applications. Firstly, raw GPS measurements from a global cluster of International GNSS Service (IGS) stations are corrected for the effect of second-order IONO. The corrected data sets are then used as input to the Bernese GPS software to estimate the precise orbit, satellite clock corrections, and Global Ionospheric Maps (GIMs). It is shown that the effect of second-order IONO on GPS satellite orbit ranges from 1·5 to 24·7 mm in radial, 2·7 to 18·6 mm in along-track, and 3·2 to 15·9 mm in cross-track directions, respectively. GPS satellite clock corrections, on the other hand, showed a difference of up to 0·067 ns. GIMs showed a difference up to 4·28 Total Electron Content Units (TECU) in the absolute sense and an improvement of about 11% in the Root Mean Square (RMS). The estimated precise orbit clock corrections have been used in all of our PPP trials. NRCan's GPSPace software was modified to accept the second-order ionospheric corrections. To examine the effect of the second-order IONO on the PPP solution, new data sets from several IGS stations were processed using the modified GPSPace software. It is shown that accounting for the second-order IONO improved the PPP solution convergence time by about 15% and improved the accuracy estimation by 3 mm.

With most tele-operated robots the operator's only feedback is the view from an onboard camera. Live video lets the operator observe the robot's immediate surroundings but does not establish the orientation or whereabouts of the robot in its environment. An additional plot of the robot's trajectory would be helpful for the operator and is sometimes provided, based on GPS. However, indoors where GPS is unavailable, tracking has to rely on dead-reckoning, which is too inaccurate to be useful. Our proposed TelOpTrak method corrects dead-reckoning errors even when only odometry and a low-cost (and thus, high-drift) MEMS-class gyro are available on the robot. TelOpTrak corrects gyro drift by exploiting the structured nature of most buildings, but without having to directly sense building features. This paper explains the TelOpTrak method and provides comprehensive experimental results.

Earlier versions of this paper (Borenstein et al., 2010a), (Borenstein et al., 2010b) were presented at two conferences. The main difference between the earlier conference papers and the present manuscript is that the latter is more comprehensive, more up-to-date, and it presents an entirely new set of experimental results, including results of a live demonstration at the 2010 Robotics Rodeo event at Ft. Benning, USA.