ICAO safety standards require low probabilities of collision of the order of 5×10−9 per hour. Such low probabilities are virtually impossible to confirm through simulations, implying the need for alternative and related safety metrics, which are easier to use. Several such alternative safety metrics are discussed in this paper. For example, it is shown that if the r.m.s. position error σ is less than about one-tenth L/σ ∼ 10 of the minimum separation distance L, then the probabilities of collision will be less than the ICAO standard, in the case of aircraft flying in opposite directions on parallel tracks. This result is derived from an analytical formula based on the statistical application of a Gaussian probability distribution to a worst-case collision scenario and a rather different result L/σ ∼ 20 arises for a Laplace probability distribution. The implication is that the ICAO standard of low probability of collision can be satisfied, by checking that the r.m.s. position error does not exceed a given value, though that value is dependent on the shape of the ‘tail’ of the probability distribution. Whether the condition is met can be checked in simulations, by measuring the drift between the intended and actual trajectory, due to all factors (navigation inaccuracy, atmospheric disturbances, trajectory drift between position updates, etc.). Thus the r.m.s. deviation from the intended trajectory can be used as a safety metric, as an alternative to the probability of collision, using the formulas and tables provided. The formulas concern a variety of possible safety metrics, including the maximum and cumulative probabilities of coincidence, probabilities of overlap, collision rates and collision probabilities; the tables apply to horizontal and vertical separation in controlled and transoceanic airspace. The sensitivity of the results to the probability distribution assumed (Gaussian or Laplace) suggests the introduction of a parametric family exponential of probability distributions, of which these are particular cases. A choice of the parameter is given that could lead to a probability distribution with a ‘tail’ shape more suited to typical Air Traffic Management (ATM) scenarios than the Gaussian and Laplace distributions, while being simpler than multi-parameter distributions.

The focus here is on the performance of and interaction between the Traffic Alert and Collision Avoidance System (TCAS) and the controller's short-term conflict alert (STCA) system. The data source used is UK Airprox Board Reports of close encounters between aircraft, and the focus is on commercial air transport aircraft using UK controlled airspace with a radar service. Do the systems work well together? Are controllers surprised when they find out that a pilot has received a TCAS resolution advisory? What do TCAS and STCA events say about collision risk? Generally, the systems seem to work together well. On most occasions, controllers are not surprised by TCAS advisories: either they have detected the problem themselves or STCA has alerted them to it. The statistically expected rate of future mid-air collisions is estimated by extrapolation of Airprox closest encounter distances.

This paper presents the results of a new multipath mitigating antenna “V-Ray” for use with terrestrial ranging signals in severe multipath indoor environments. The V-Ray antenna – as used in the Locata positioning system – forms tight beams that provide line-of-sight range measurements as well as azimuth measurements. To take advantage of these two types of measurements a new navigation algorithm – Position and Attitude Modelling System (PAMS) – is proposed for processing carrier phase and azimuth measurements via an unscented Kalman filter. The PAMS can output the complete navigation parameters of position, velocity, acceleration and attitude simultaneously. The indoor test was conducted in a metal warehouse and the results confirmed that the horizontal positioning solutions had an accuracy of better than four centimetres and an orientation accuracy of better than 1°.

The LAMBDA method for integer least-squares ambiguity resolution has been widely used in a great variety of Global Navigation Satellite System (GNSS) applications. The popularity of this method stems from its numerical efficiency and its guaranteed optimality in the sense of maximising the success probability of integer ambiguity estimation. In the past two decades, the LAMBDA method has been typically used in cases where the number of ambiguities is less than several tens. With the advent of denser network processing and the availability of multi-frequency, multi-GNSS systems, it is important to understand LAMBDA's performance in high dimensional spaces. In this contribution, we will address this issue using real GPS data based on the Bernese software. We have embedded the LAMBDA method into the Bernese software and compared their ambiguity resolution performances. Twelve day dual-frequency GPS data with a sampling interval of 30 s was used in the experiment, which was collected from a network of 19 stations in the Perth area of Western Australia with an average baseline length of 380 km. Different experimental scenarios were examined and tested with different observation spans, which represent the different ambiguity dimensions. The results showed that LAMBDA is still efficient even when the number of ambiguities is more than 100, and that the baseline repeatability obtained with the ambiguities resolved from the LAMBDA method agreed well with that of Bernese. Therefore, for future dense network processing, the easy-to-use LAMBDA method should be considered as an alternative to baseline-per-baseline methods as those used in e.g. the Bernese software.

With the characteristics of full autonomy and no accumulated errors, polarisation navigation shows tremendous prospects in underwater scenarios. In this paper, inspired by the polarisation vision of aquatic organisms, a novel point-source polarisation sensor with high spectral adaptability (400 nm–760 nm) is designed for underwater orientation. To enhance the environmental applicability of the underwater polarisation sensor, a novel sensor model based on the underwater light intensity attenuation coefficient and optical coupling coefficient is established. In addition, concerned with the influence of light intensity uncertainty on sensor performance underwater, an antagonistic polarisation algorithm is adopted for the first time, to improve the accuracy of angle of polarisation and degree of polarisation in the low signal-to-noise ratio environment underwater. Finally, indoor and outdoor experiments are carried out to evaluate the performance of the designed polarisation sensor. The results show that the designed point-source polarisation sensor can acquire polarised light and be used for heading determination underwater.

This paper describes the first of a two-part research effort to find the optimal detector and estimator that minimise the integrity risk in Receiver Autonomous Integrity Monitoring (RAIM). In this first part, a new method is established to determine a piecewise linear approximation of the optimal detection region in parity space. The paper presents examples suggesting that the optimal detection boundary lays in between that obtained using chi-squared residual-based RAIM, and that provided by Solution Separation (SS) RAIM, as one varies the alert limit requirement. In addition, these examples indicate that for realistic navigation requirements, the SS RAIM method approaches the optimal detection region. The SS RAIM detection tests will be employed in the second part of this work, which focuses on the design of non-least-squares estimators to reduce the integrity risk in exchange for a slight increase in nominal positioning error.

The probability of failure (failure rate) is a key input parameter to integrity monitoring systems used for safety, liability or mission critical applications. A standard approach in the design of Global Positioning System (GPS) integrity monitoring is to utilise the service commitment on the probability of major service failure, often by applying a conservative factor. This paper addresses the question of what factor is appropriate by applying Bayesian inference to real and hypothetical fault histories.

Global Navigation Satellite System (GNSS) anomalies include clock or signal transmission type faults which are punctual (may occur at any time) and incorrect ephemeris data which are broadcast for a nominal two hours. These two types of anomaly, classified as continuous and discrete respectively are addressed. Bounds on the total probability of failure are obtained with given confidence levels subject to well defined hypotheses relating past to future performance. Factors for the GPS service commitment of 10−5 per hour per satellite are obtained within the range two to five with high confidence (up to 1–10−9).

Tactical monitoring and controlling of air traffic is becoming increasingly difficult to manage for Air Traffic Controllers (ATCOs) owing to an increasingly complex traffic flow. A dynamic tactical complexity model, herein known as Conflict Activity Level (CAL), has been developed and is presented in this paper. This can be achieved either by establishing an overall score for an entire region or sub-regions of interest as specified by user's input location and time. This is done by evaluating the likely aircraft flight shape profile based on its current and projected position and trajectory. From the flight shape profile, CAL values are computed based on instantaneous existing traffic numbers in the overall region or sub-regions of interest. The proposed complexity approach shows good agreement with other methods in terms of ranking the order of complexity of various air traffic scenarios and the key influencing factors contributing to conflict.

The Carrier-Phase (CP) technique used in the Global Positioning System (GPS) has proved to be a useful spatial tool for remote precise time transfer. Galileo is a Global Navigation Satellite System like GPS. However, currently, given the low number of satellites at any one observation epoch, Galileo's accuracy and continuity of time transfer leave much to be desired. To achieve better performance of time transfer for Galileo, this study has developed a new approach for Galileo CP time transfer, using prior constraint information such as precise coordinates and troposphere zenith delay constraints. The new approach was applied for precise time transfer in real-time mode and post-processed mode for short baseline and long baseline observations. For the short baseline time link in real-time mode, compared with the standard Galileo CP, the standard deviation improved by 51·4% for the troposphere zenith delay constraint, 47·6% for the station coordinates constraint, and 49·5% when considering both constraints simultaneously. At a 10,000 s time interval, in comparison to the standard CP, the three constraint approaches show stable results as well as improvements of nearly an order of magnitude. In post-processed mode, the constraint approach for Galileo time transfer showed little improvement compared to the standard CP technique for both the short baseline and long baseline time links.

This paper reports on innovative mathematical and analytical approaches to celestial navigation. Beyond the common-sense recommendation for automation of the calculations, it is necessary to consider the specific algorithms used. The advantages of these new algorithms become evident when navigational practice is extended beyond the usual twilight round of sights or the noon Sun line. But exploiting the full advantages of the algorithms would probably require new software. This leads us to consider the prospects of applying new information technologies to the task of taking celestial observations.

Pedestrian dead reckoning (PDR) is widely used in handheld indoor positioning systems. However, low-cost inertial sensors built into smartphones provide poor-quality measurements, resulting in cumulative error which consists of heading estimation error caused by gyroscope and step length estimation error caused by an accelerometer. Learning more motion features through limited measurements is important to improve positioning accuracy. This paper proposes an improved PDR system using smartphone sensors. Using gyroscope, two motion patterns, walking straight or turning, can be recognised based on dynamic time warp (DTW) and thus improve heading estimation from an extended Kalman filter (EKF). Joint quasi-static field (JQSF) detection is used to avoid bad magnetic measurements due to magnetic disturbances in an indoor environment. In terms of periodicity of angular rate while walking, peak–valley angular velocity detection and zero-cross detection is combined to detect steps. A step-length estimation method based on deep belief network (DBN) is proposed. Experimental results demonstrate that the proposed PDR system can achieve more accurate indoor positioning.

This contribution extends the common documented approach of integrity through Protection Levels in Satellite-Based Augmentation System (SBAS) positioning for aeronautics, to reliability on the basis of statistical hypothesis testing, and as such provides a safeguard against model misspecifications as anomalies and outliers in the measurements. It is shown that when integrity is monitored through Protection Levels and reliability added through Reliability Levels, the availability of the SBAS position solution is more than 99% for APV-I precision approach. The availability for CAT-I is currently just a few percent. When the Galileo constellation is added, and current performance is copied ahead, the percentage for CAT-I increases to beyond 95%.

Global satellite navigation systems have been under development by the United States and the Soviet Union for many years. The US Navstar GPS system saw its first launch in 1978 and the USSR's Glonass system followed 4 years later. The US space shuttle, which was foreseen as the launch vehicle for Navstar spacecraft, received an enormous setback in 1986 as a result of the Challenger accident. In the meantime, Glonass launches, which carry three spacecraft at once into orbit, have proceeded without incident (until the failure on 24 April 1987). Both systems are currently still in test phase and can be expected to reach operational status in 3 or 4 years' time. In the meantime, the idea of combining Navstar and Glonass into a single civil programme has many attractions for all concerned. Some aspects of Glonass orbital characteristics and signal structure are discussed with this end in view. In addition, features of the data message content of Navstar and Glonass are also compared, to gain a better understanding of the feasibility of a dual satellite navigation system.

Over the past seventy years many advances have been made in the field of ship control. Early developments by Sperry and Minorsky on proportional controllers have led to today's modern control systems which have interfacing capabilities with position fixing equipment.

This paper presents a brief historical summary of the methods employed in ship control from early proportional devices through the range of adaptive systems and concludes with details of a possible future control method known as intelligent control.

Intelligent control consists of three methodologies: expert, fuzzy and neural. An investigation and comparison of the methodologies will present possible future control strategies.

The precise autonomous navigation for deep space exploration by combination of multi-source observation data is a key issue for probe control and scientific applications. In this paper, the performance of an integrated Optical Celestial Navigation (OCN) and X-ray Pulsars Autonomous Navigation (XNAV) system is investigated for the orbit of Mars Pathfinder. Firstly, OCN and XNAV single systems are realised by an Unscented Kalman Filter (UKF). Secondly, the integrated system is simulated with a Federated Kalman Filter (FKF), which can do the information fusion of the two subsystems of UKF and inherits the advantages of each subsystem. Thirdly, the performance of our system is evaluated by analysing the relationship between observation errors and navigation accuracy. The results of the simulation experiments show that the biases between the nominal and our calculated orbit are within 5 km in all three axes under complex error conditions. This accuracy is also better than current ground-based techniques.

The problem of indoor navigation is investigated using a Commercial Off-the-Shelf (COTS) pseudolite system. The system is operated in synchronous and asynchronous mode. It is shown that, when the system is operated in synchronous mode, it is unsuitable for deep indoor operations: in complex propagation environments, the synchronisation required for metre level navigation is difficult to achieve and different solutions have to be adopted. Two asynchronous approaches are thus considered and indoor navigation with metre level accuracy is demonstrated using C/N0 measurements. The approaches use a modified Receiver Signal Strength (RSS) navigation algorithm and a weighted centroid technique, respectively. In both cases, a pre-filtering stage has been adopted to enhance the quality of C/N0 measurements. The two methods have been compared under different operating conditions and the advantages and drawbacks of the two techniques have been analysed. The experiments demonstrate that metre level accuracy can be achieved using asynchronous pseudolites. These results are particularly encouraging since they were obtained without exploiting map constraints and prior knowledge of the user position.

Ultra Short Baseline (USBL) navigation systems are often faced with positioning errors arising from misalignments between sensors. This paper proposes a line survey method for USBL angular alignment calibration. In the scheme of USBL line survey, mathematical representations of positioning error arising from heading, pitch and roll misalignments are derived, respectively. The effect of each misalignment angle and how the differences can be used to calibrate each misalignment angle in turn are presented. An iterative algorithm that takes advantage of the geometry of position errors resulting from angular misalignments is developed for USBL calibration. Numerical simulations are provided to demonstrate the effectiveness of the USBL line survey approach. In addition, the effect of measurement error on the estimation of roll alignment error is evaluated and discussed.

Exact motion estimation is a major task in autonomous navigation. The integration of Inertial Navigation Systems (INS) and the Global Positioning System (GPS) can provide accurate location estimation, but cannot be used in a GPS denied environment. In this paper, we present a tight approach to integrate a stereo camera and low-cost inertial sensor. This approach takes advantage of the inertial sensor's fast response and visual sensor's slow drift. In contrast to previous approaches, features both near and far from the camera are simultaneously taken into consideration in the visual-inertial approach. The near features are parameterised in three dimensional (3D) Cartesian points which provide range and heading information, whereas the far features are initialised in Inverse Depth (ID) points which provide bearing information. In addition, the inertial sensor biases and a stationary alignment are taken into account. The algorithm employs an Iterative Extended Kalman Filter (IEKF) to estimate the motion of the system, the biases of the inertial sensors and the tracked features over time. An outdoor experiment is presented to validate the proposed algorithm and its accuracy.

Hairawa in the Journal made the statement that there is no easy method of calculating the length of a geodesic line on the surface of a spheroid and this is true. Nevertheless, it is the purpose here to attempt to devise a method and then to leave it to the reader to judge whether or not the amount of work involved justifies the method as an alternative to the correction methods of Andoyer and Lambert and to the work of Hairawa himself.

Traditionally, on a great circle, the latitude or longitude of a waypoint is found by inspection. In this paper, using an elementary knowledge of vector algebra including linear combination of vectors and vector basis, we provide an easy method for finding the equation of a great circle path as a parameterized curve. By use of this vector function of distance travelled, the latitude and longitude of waypoints can be found based on the distance from departure point along a great circle. The approach is intended to appeal to the navigator who is interested in the mathematics of navigation and who, nowadays, solves his navigation problems with a personal computer.