This paper examines the evolution of the arctic submarine and the ever-increasing scientific and commercial potential which have accompanied this evolution over the past 340 years. It is a sporadic history of arctic submarine ideas, concepts and actual experiences with vessels at sea. It happens to be a history that is largely American, with important additions as a result of the experiences of the Germans, Soviets and the British, particularly during World War II. Finally, it is a history in which five early visionaries in particular stand out: Bishop John Wilkins of England; Jules Verne of France; Professor Anschutz-Kampfe of Germany; the submarine designer Simon Lake, of the United States — whose influence extended over four decades until well into the twentieth century; and Sir Hubert Wilkins of Australia.

Determination of calibration parameters is essential for the fusion performance of an inertial measurement unit (IMU) and odometer integrated navigation system. Traditional calibration methods are commonly based on the filter frame, which limits the improvement of the calibration accuracy. This paper proposes a graph-optimisation-based self-calibration method for the IMU/odometer using preintegration theory. Different from existing preintegrations, the complete IMU/odometer preintegration model is derived, which takes into consideration the effects of the scale factor of the odometer, and misalignments in the attitude and position between the IMU and odometer. Then the calibration is implemented by the graph-optimisation method. The KITTI dataset and field experimental tests are carried out to evaluate the effectiveness of the proposed method. The results illustrate that the proposed method outperforms the filter-based calibration method. Meanwhile, the performance of the proposed IMU/odometer preintegration model is optimal compared with the traditional preintegration models.

The problem of errors in radar plotting were considered by Capt. H. Topley (11, 167) and Capt. F. J. Wylie (12, 198), and it was shown that the error in the estimated distance of the C.P.A. depends upon mean range and range change in plotting interval. I want to introduce the term rate of error in the estimated distance of C.P.A., in the same way that Topley shows the percentage error in the estimated speed.

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.

Carrier-phase inter-frequency bias (IFB) exists in GLObal NAvigation Satellite System (GLONASS) baselines when receivers of different brands are used. Those biases need to be calibrated in GLONASS data processing to derive precise fixed solutions. Consequently, the accuracy of the IFB calibration affects ambiguity fixing, and low-accuracy IFB values in the calibration will degrade the positioning results. Hitherto, at least two IFB rate value sets for various receiver brands have been given in previous studies. Some of the differences between the value sets exceed 2 mm/FN (frequency number) and the effects of those differences on ambiguity fixing have not been investigated until now. This study showed that ambiguity fixing in GLONASS single-epoch positioning is very sensitive to the accuracy of the IFB rates. Even errors of millimetres can seriously lower the empirical success rate. The short baselines from the Global Navigation Satellite System (GNSS, which includes Russian GLONASS) networks of the International GNSS Service and the Regional Reference Frame Sub-Commission for Europe were employed to obtain more accurate IFB rate estimates with the proposed two-dimensional particle filtering. Afterwards, the IFB estimates were statistically refined by the least-squares method. Experiments showed that when the refined IFB rates were used in the IFB calibration, the empirical success rates of ambiguity fixing in GLONASS single-epoch positioning were largely improved compared with the values given before, improvements such as 20·6% for a Septentrio and Leica receiver combination.

The upcoming GNSS Galileo, with its new satellite geometry and frequency plan, will not only bring many benefits for navigation and positioning but also help to improve ionosphere delay estimation. This paper investigates ionosphere estimation with Galileo and compares it with the results from GPS-only and combined GPS-Galileo. The standard deviation of the Vertical Total Electron Content (VTEC) at a certain location can improve significantly by 40 per cent. Various Galileo configurations are considered to assess the differences in frequency plan and signals to be used. The IGS network, which is involved in producing the current IGS Global Ionosphere Map (GIM) is used in the simulation for more realistic results. A more accurate GIM will in its turn improve navigation and positioning performance.

The switching between a damped and an undamped Inertial Navigation System (INS) is an important technical method to ensure its long-term accuracy. The stability of switching is of great importance. This paper studies the switching stability problem between a damped and an undamped INS. A model of an inertial navigation switching system is established by introducing switched control. The average dwell time method is used to analyse stability and a sufficient condition of exponential stability is given. The condition is also extended to the switched system containing constant disturbance and the sufficient condition of exponential stability. The effect of introducing switched control for the smooth operation of the system is verified and the accuracy of a long-term INS is improved effectively.

Oscillator phase noise has a negative effect on the tracking performance of Global Navigation Satellite System (GNSS) receivers. To provide GNSS software receivers with real test environments, this paper proposes a method to simulate the GNSS Intermediate Frequency (IF) signal, taking the oscillator phase noise effect into consideration. The oscillator parameters are first measured via a pseudolite transmitter and receiver system. According to the measured oscillator parameters, an oscillator-induced frequency fluctuation is then generated, and added to the digital IF signal. Further simulation experiments are conducted that attempt to measure the oscillator phase noise effect on a second-order Phase Lock Loop (PLL) performance. Results indicate that the IF signal simulator considering the oscillator phase noise is able to provide software receivers with real signal dynamics, helping to evaluate the performance of signal processing algorithms on a software platform.

Future air navigation envisages increased use of Global Navigation Satellite Systems (GNSS) together with advanced communications and surveillance technologies to facilitate the required increase in capacity, efficiency and safety without adversely impacting the environment. The full benefit of GNSS is expected from its ability to support en-route to en-route or gate-to-gate air navigation. This presents challenges particularly for the phases of flight with stringent required navigation performance. Significant work has so far been devoted to the phases of flight up to CAT I. However, more work is required for CAT III precision landing (with an accuracy requirement at the metre level) and taxiing (with an accuracy requirement at sub-metre level) and both with very high integrity and continuity requirements. The main limitation in using GBAS for CAT III landings is the potential decorrelation of the measurement errors between the GBAS ground station (GGS) and the user. The threats in this respect are the atmospheric anomalies. Periods of strong solar activity can cause large local spatial and temporal gradients in the delays induced on the GNSS signals by the ionosphere. The local nature of the effects results in significant decorrelation between GGS measurements and the user. Therefore, a reliable ground based ionospheric anomaly monitoring scheme is required to guarantee integrity.

This paper critically reviews state-of-the-art monitors, identifies their limitations and addresses them by proposing a high-performance monitoring scheme for the ionosphere. Preliminary analyses suggest that the proposed scheme has the potential to enable GNSS to meet the navigation requirements for CAT III and taxiing.

In designing and developing navigation receiver embedded software, the correct scheduling of navigation tasks is critical for ensuring that a receiver works in the right way. If a receiver's timing scheduling becomes abnormal, it may lead to timing conflicts of the multi-tasking navigation receiver, which may seriously influence the system's performance of real-time features and functionalities. This paper models the timing scheduling of navigation receivers by extracting all important timing parameters including the execution time, period, deadline and priority etc., and focusing on the execution time. The maximum execution time of a navigation task relies on the design and implementation algorithms and the computing capability of the processor. The execution time parameter can be properly adjusted in receiver software design or even in the phase of the receiver requirement changes. On the other hand, the other parameters (i.e., the period, deadline and priority) mainly depend on the receiver's technical requirements, and usually these parameters are set to constant values. In this research, a novel off-line method based on the maximum allowed execution time dichotomy optimization is proposed, and the equilibrium rule is proposed to apply to the multi-task maximum allowed execution time dichotomy search and an analysis of time series of those parameters obtained from real observations of receiver tasks was also conducted. Results indicate that the relative equilibrium is more suitable to the multi-task scheduling of receiver navigation, compared to the absolute equilibrium. The proposed method provides a fast off-line scheduling approach for the top level task design of navigation receivers, and remarkably improves the development efficiency of receiver embedded software.

This and the following paper were first presented at NAV 2000 on Thursday, 2 November 2000 – the day devoted to Location and Communication for Land Vehicles.

This paper discusses the need for Intelligent Transport Systems (ITS) and the key factors influencing the Government's Integrated Transport Policy. Typical ITS projects and applications in the UK are reviewed and conclusions drawn.

K. H. Zevering has recently proposed a way to calculate the position of a moving observer, from the intersection of position circles, that differs from the methods hitherto accepted by mariners1. Zevering concludes, from discrepancies between his own results and that of other methods, that those others are in error. However, the discrepancies result from incorrect assumptions in his proposed method, which give rise to erroneous answers. My comments will be restricted to the simplest case of two observations only, and will assume that the Earth is, for our purposes, spherical.

In this paper, two algorithms of Global Positioning System based attitude determination are proposed. The first algorithm extends the Kalman filter approach to determine the integer ambiguity and the orientation that is needed in a typical gps-based attitude determination problem. The second algorithm explores the mean field annealing neural network approach, which is a combination of the competitive Hopfield neural network and the stochastic simulated annealing technique, to resolve the optimal attitude problems. A test platform is set up for verifying these algorithms. The two algorithms are further compared in terms of computation speed and convergence rate.

This and the following paper were first presented at the RIN01 Conference held in Oxford under the auspices of the Animal Navigation Special Interest Group, April 2001.

Flight paths of homing pigeons were measured with a newly developed recorder based on GPS. The device consists of a GPS receiver board, a logging facility, an antenna, a power supply, a DC-DC converter and a casing. It has a weight of 33 grams and works reliably with a sampling rate of 1 Hz for an operating time of about three hours, providing time-indexed data on geographic positions, ground speed and altitude. The devices are fixed to the birds with a harness, and the data are downloaded when the bird is re-captured. The measured flight paths show many details : for example, initial loops flown immediately after release and large detours flown by some pigeons. Three examples of flight paths are presented from a release site 17·3 km northeast of the home loft in Frankfurt. Mean speed in flight, duration of breaks and total length of the flight path were calculated. The pigeons chose different routes and have different individual tendencies to fly loops over the village close to the release site.

I am pleased to see that, in light of my critical evaluation, Arne B. Molander has reevaluated a number of points in his analysis, and has revised his proposals of Columbus's alleged use of the Moon for determining his longitude. However, it is disappointing that these latest proposals again do not seem to have been thoroughly considered.

Since it is clear that Columbus's East–West position fixes are not correlated with visible lunar-planetary conjunctions, Mr Molander's latest hypothesis is that Columbus observed a dark-horizon moonrise or moonset near each conjunction – which usually can be done whether or not the conjunction itself is visible. However, it is entirely unclear how such an observation can be converted into a longitude. Reading attentively, we can glean a few details of this process: only a single observation is required, since some positions are computed within a few hours of the purported observation; and Columbus apparently used the Ephemerides of Johann Miiller, since errors in that ephemeris are alleged to have caused errors in the computed longitude. In his 1992 paper, Mr Molander asserted that timing of the conjunction is not required by this method, because Columbus somehow utilizes the Moon's daily topocentric motion. But how this datum is utilized, and in fact all details of the longitude determination itself, are entirely obscure.

Knowledge of the statistics of aircraft vertical speeds is important both for the construction of realistic traffic simulators and for the development of trajectory prediction tools for use in future air traffic control (ATC) systems. This paper reports on the analysis of radar data recordings for nearly 10000 civil flights on airways. Results are presented for the means and spreads of vertical speeds as functions of altitude. Evidence is presented that roughly half of the observed spreads arise from fluctuations within each aircraft's trajectory, as opposed to variation from one aircraft to another. A simple procedure is proposed for simulating vertical speed data which has statistics similar to those obtained from the radar recordings. Some consequences of the results for the development of trajectory prediction tools for use in future ATC systems are discussed. The results suggest that the provision of accurate trajectory prediction tools is not as straightforward as it might at first appear to be.

This paper was first published in 1960 (Vol. 13, p. 127). It is followed by comments from John Kemp. The paper has been abridged, including the omission of section 5 which described a proposal for a new radar display.

When the problem of collision in the air is discussed, it is usual to start by pointing out the enormous closing speed of two modern aircraft meeting head-on, and to conclude from this that avoidance on the ‘see and be seen’ principle has ceased to be possible. The fact is, however, that the great majority of mid-air collisions (about 85 percent) occur within five miles of an airport and the typical case is not the head-on one, but the case in which the two aircraft crab into one another from a direction which may be anywhere around the whole enclosing sphere. Since the field of view of the aircrew covers only about 20 percent of the enclosing sphere, the aircrew of colliding aircraft seldom see each other. It would seem, therefore, that the ‘see and be seen’ principle never did afford much protection, even when speeds were low. In other words, the fact that the number of mid-air collisions in Europe has hitherto been small is not primarily due to seeing and evading, although this sometimes happens, but to the fact that the airspace is very large compared to the volume of all the aircraft in it at any given time. However, as traffic densities go up, the risk rapidly increases, and in congested airspace, such as that around New York, the problem of avoiding collision has already become acute. In the period 1948–57, there were 159 mid-air collisions in the United States, and many of these made headlines in the world press. One can imagine the public outcry if two large transports were to collide over a housing estate; but unless something effective is done, something like this will presumably happen eventually. At very high altitudes the ‘see and be seen’ principle certainly fails, by day, because the speed will be high, and in addition, the range at which a pilot can see an object the size of an aircraft may be less than 1½ miles due to what is sometimes called ‘high-altitude myopia’.

In this paper, a simplified constellation architecture consisting of only two navigation satellites located around the Earth-Moon L1,2 libration points is obtained for the Universe Lighthouse. In order to determine the feasible constellations that can achieve continuous global coverage for lunar orbits, an exhaustive search over all possible combinations of libration point orbits is performed first. With the use of a fitting procedure, amplitude relations between the feasible L1 and L2 libration point orbits are derived by polynomial interpolation. After that, a cislunar navigation simulation is conducted to verify the navigation performance of the candidate two-satellite constellations. The final Monte Carlo simulation results indicate that the simplified system is available for cislunar navigation and the best accuracy of a few tens of metres can be achieved for both the trans-lunar cruise phase and lunar orbit phase.

We proposed an adaptive H-infinity Cubature Kalman Filter (AH∞CKF) to improve the navigation accuracy of a highly manoeuvrable unmanned aerial vehicle (UAV). AH∞CKF fuses the Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS) measurements. Traditional state estimation filters like extended Kalman filters (EKF) and cubature Kalman filters (CKF) assume Gaussian noises. However, their performance degrades for non-Gaussian noises and system uncertainties encountered in real-world applications. Thus, designing filters robust to noise and distribution is crucial. AH∞CKF combines H∞CKF design with an added adaptive factor to adjust the state estimation covariance matrix according to measurements by exploiting the square root method to yield more numerically stable results (SrAH∞CKF). We conducted multiple dynamically rich flight tests to validate our claims using a UAV equipped with a commercially well-known GNSS solution. Results show that the SrAH∞CKF state estimation outperforms EKF and CKF methods on average by 90% in various statistical measures.