Celestial navigation is an important type of autonomous navigation technology which could be used as an alternative to Global Navigation Satellite Systems (GNSS) when a vessel is at sea. After several centuries of development, a variety of astronomical vessel position (AVP) determination methods have been invented, but the basic concepts of these methods are all based on angular observations with a device such as a sextant, which has disadvantages including low accuracy, manual operation, and a limited period of observation. This paper proposes a new method that utilises a fisheye camera to image the celestial bodies and horizon simultaneously. Then, we calculate the obliquity of the fisheye camera's principal optical axis according to the image coordinates of the horizon. Next, we calculate the altitude of the celestial bodies according to the image coordinates of the celestial bodies and the obliquity. Finally, the AVP is determined by the altitudes according to the robust estimation method. Experimental results indicate that this method not only could realize automation and miniaturization of the AVP determination system, but could also greatly improve the efficiency of celestial navigation.

The next generation Global Navigation Satellite Systems (GNSS), such as Galileo and Global Positioning System (GPS) modernization, will use signals with equal code and bit periods, resulting in a potential bit sign transition in each primary code period of the received signal segments. A bit sign transition occurring within an integration period usually causes a splitting of the Cross Ambiguity Function (CAF) main peak into two smaller side lobes along the Doppler shift axis in the search space and it may lead to an incorrect Doppler shift estimate, which results in a serious performance degradation of the acquisition system. This paper proposes a novel two steps based bit sign transition cancellation method which can overcome the bit sign transition problem and remove or mitigate the CAF peak splitting impairments. The performance of the proposed technique has been comprehensively evaluated with Monte Carlo simulations in terms of detection and false alarm probabilities, which are presented by Receiver Operating Characteristic (ROC) and Signal-to-Noise-Ratio (SNR) curves. The test results show that the proposed acquisition technique can provide improved performance in comparison with the state-of-the-art acquisition approaches.

The purpose of this paper is to show the effect of incorporating various discrete grid systems in a micro-based, ship weather-routeing system, which employs Bellman's dynamic programming algorithm, and either a cost-objective or time-objective performance measure. A simple ship speed and power function is utilized, in the cost computation. The calculation of the least-cost/least-time route is briefly described, but it is the derivation of the discrete grids and their influence on the route decisions that forms the paper's emphasis. The measure of cost within this paper is necessarily notional.

To solve the problem of identifying ship model parameters quickly and accurately with the least test data, this paper proposes a nonlinear innovation parameter identification algorithm for ship models. This is based on a nonlinear arc tangent function that can process innovations on the basis of an original stochastic gradient algorithm. A simulation was carried out on the ship Yu Peng using 26 sets of test data to compare the parameter identification capability of a least square algorithm, the original stochastic gradient algorithm and the improved stochastic gradient algorithm. The results indicate that the improved algorithm enhances the accuracy of the parameter identification by about 12% when compared with the least squares algorithm. The effectiveness of the algorithm was further verified by a simulation of the ship Yu Kun. The results confirm the algorithm's capacity to rapidly produce highly accurate parameter identification on the basis of relatively small datasets. The approach can be extended to other parameter identification systems where only a small amount of test data is available.

The fingerprint positioning (FP) algorithm has been investigated extensively owing to the fact that it can provide a relatively ideal indoor positioning result. However, the effectiveness of the fingerprint algorithm relies on the size of fingerprint database, which prevents the algorithm from being widely applied in practical applications. In this paper, an improved fingerprint algorithm with access point (AP) selection strategy and reference point (RP) selection strategy is proposed to reduce the size of the fingerprint database and improve the positioning accuracy. The experimental results show that the proposed algorithm can reduce the storage size of the fingerprint database by more than 42·64%. Moreover, compared with the FP algorithm, the fingerprint algorithm with segment characteristic distance (FP-SCD) and the fingerprint algorithm with RP selection strategy (FP-RPSS), the average positioning error of the proposed algorithm is reduced by 20·15%, 10·83% and 11·57%, respectively. Therefore, the proposed algorithm has a good application in real positioning scenarios.

This paper presents a framework for a strapdown Inertial Navigation System (INS) algorithm design by using Lie group and Lie algebra. The general way to solve Lie group differential equations is introduced. Investigations reveal that this general Lie group method provides a simpler unified way to solve differential equations involving direction cosine matrix, quaternion and dual quaternion, which are widely used in INS algorithm design. Furthermore, we also present a new INS algorithm based on the Special Euclidean group se(3) under the guidelines of Lie group method. Analyses show that se(3) algorithm has the same accuracy as a dual quaternion algorithm, this is also justified by numerical simulations. Though the se(3) algorithm has no improvements in accuracy, the general Lie group method used in the design process shows its brevity and uniformity.

Recent evidence has shown that the effect of a ship moving in shallow water and the resultant squat are not well understood. This paper reviews the general problem of a ship in shallow water and illustrates the corresponding resistance, trim and sinkage at both sub-critical and also at super-critical speeds.

The paper then reviews the various methods of predicting the squat of a ship in shallow water in the sub-critical range, which is applicable to most ships. It is suggested that the simple rule-of-thumb methods are, at best, unreliable and the paper gives examples of empirical methods which have been tested against various sets of data and seem to give more representative answers. A summary of the notation used is given at the end of the paper.

An escort tugboat comes to the aid of a vessel when that vessel is navigating in confined waters and at a speed that is usually higher than six knots. In the escort manoeuvre, two systems come into play. One is the propulsion and steering of the vessel. The other involves the tug winch in terms of the tension it exerts and the length of towline released. In this way, the tug winch becomes a key piece of equipment. Along with the difficulties of carrying out the manoeuvre itself are the risks resulting from the operation of the winch. For this reason, automatic manoeuvring systems have been developed to facilitate this operation. They consist of information technology applications that help the skipper with manoeuvring the tug. At the same time, they make it possible to display and monitor the most important parameters of the towing winch. This study will describe a control system for the towline so that it can help carry out the towing manoeuvre with an escort tug. It indicates the control parameters for the manoeuvre, as well as the operational variables of the winch on which the system runs.

A prerequisite for a Global Positioning System (GPS) attitude determination is to calculate baselines between antennae with accuracy at the millimetre level simultaneously. However, in order to have a low cost attitude determination system, a set of Commercial-Off-The-Shelf (COTS) receivers with separate clocks are used. In this case, if the receiver clocks are not precisely synchronized, the baseline vector between antennae will be calculated from the GPS signals received at different times. This can be a significant error source for high-kinematic applications. In this paper, two equivalent and effective approaches are developed to compensate this significant bias for baseline estimation and attitude determination. Test results using real airborne GPS data demonstrate that the receiver time misalignment between the two receivers can result in a 5 cm baseline offset for an aircraft with a 50 m/s velocity; the corresponding attitude errors can reach about 0·50° in yaw and 0·10° in pitch respectively for the attitude determination system with a baseline length of 3·79 m. With the proposed methods, these errors can be effectively eliminated.

The remarkably successful development in recent years of inertial navigation systems suggests a reconsideration in this light of the phenomenon of animal navigation, the physiological basis of which has not been fully established. Some of the aspects of inertial navigation which may be particularly relevant to possible biological analogues are considered. Aspects of animal navigation and orientation that are particularly suggestive of inertial navigation are also treated. The physiology of the biological sensory mechanisms that could form the sensing elements of the biological inertial systems are outlined. Some suggestions are advanced for further investigations.

Perhaps the most surprising thing about sea waves is that they come in a vast range of shapes and sizes. The casual observer on a ship in waters not exposed to an ocean, for example the southern North Sea, may rightly think that the waves he can see have all been generated by the same wind blowing over some particular stretch of water for a fixed length of time. It then seems almost logical to deduce that all the waves ought to be of the same height, length and shape. Unfortunately this is not the case, the energy of sea waves is locked in wave components spread over a wide range of wave periods, each of which travels at a speed dictated by its period. Considering the very simple case of a sea with only wave components, when a crest of one component overtakes the other, a higher wave will ensue. As a result of this process, high waves come in groups; during the time in which the components gradually get into phase the wave height builds up giving a train of waves of increasing, which then decreases as the faster component travels away, until when they are out of phase the sea is temporarily fairly calm. This is the reason why it is commonly said that every seventh wave is the highest, although whether it is every fourth or every fourteenth depends on the relative speeds of the components.

This paper was presented at a meeting of the Institute in London on 18 February 1981 with Dr J. F. Kemp in the Chair. Captain Alderton discusses a variety of criteria for assessing economic optimal speeds and shows how sensitive these optima are to such constraints as port time, voyage distance and bunker costs.

The expression ‘optimum’ is frequently used very loosely and one often finds that the factor under consideration is only being optimized with reference to some, not all, of its dependent variables. A truly optimum speed for a ship can only be achieved by considering:

(i) What speeds the ship can actually achieve, taking into account various mechanical constraints, the state of the hull (fouling), the draft and the effect of the weather.

(ii) What speeds we would like the ship to achieve taking into account the costs, the profits and the pressure of schedules.

In this contribution, an improved Extended Kalman Filter (EKF), named the Total Extended Kalman Filter (TEKF) is proposed for integrated navigation. It can consider the neglected random observed quantities which may appear in a dynamic model. In particular, this paper will consider the case of vision-based navigation. This algorithm is equipped with quadratic constraints and makes use of condition equations. The paper will show that the refined data from different sensors including a Global Positioning System (GPS) receiver, an Inertial Navigation System (INS) and remote sensors can be fused into a Constrained Total Extended Kalman Filter (CTEKF) algorithm. The CTEKF algorithm is applied to a case study in the Guilan province in the north of Iran. The results show the efficiency of the proposed algorithm.

There are many scenarios where an integrated INS/GNSS navigation system may be required to operate in a high interference or weak signal environment. The GPS receiver may exploit the inertial aiding by operating with narrow tracking loop bandwidths in order to increase interference resistance. However, where a low grade INS is used, wider bandwidths are desirable to calibrate the INS errors effectively. This is important for GPS tracking loop aiding and sole-means inertial navigation during jamming. To obtain both effective INS calibration and jamming resistance, an adaptive tightly-coupled (ATC) INS/GPS integration architecture has been developed. The ATC technique has been assessed by simulation, showing that it provides a significant anti-jam margin over an INS/GPS with fixed tracking bandwidths selected for INS calibration. Compared to the deep (or ultra-tightly-coupled) integration techniques currently under development, ATC is a low cost anti-jam integration technique as it does not require a complete re-design of the navigation architecture. When there is too much interference for any GNSS signals to be tracked, the INS provides sole-means navigation. Thus, it is important to optimise the calibration of the INS when GNSS signals are available. To this end, the effects of estimating higher order inertial instrument errors and satellite range biases within the INS/GPS integration filter have been assessed.

In this paper, a novel Strong Tracking Sigma-Point Predictive Variable Structure Filter (ST-SP-PVSF) is presented as a further development of the Adaptive Predictive Variable Structure Filter (APVSF) for attitude synchronisation during Satellite Formation Flying (SFF). First, the sequence orthogonal principle is adopted to enhance the robustness of the APVSF for any nonlinear system with uncertain model errors. Then, sigma-point sampling strategies (such as unscented transfer, cubature rule and Stirling's polynomial interpolation) are introduced to extend the APVSF with the ability to capture the second central moment's information on the model errors to update the system model with higher precision. The new methodology has advantages in dealing with the various types of uncertainties or model errors compared with the APVSF. In addition, it does not need to choose the limit boundary layer ψlim it for system estimation, which reduces the sensitivity to the initial parameters and improves its adaptive ability over the APVSF. Simulations are performed to demonstrate that the proposed method is more suitable for attitude synchronisation estimation of the SFF system.

Fluctuation of the received signal strength (RSS) is the key performance-limiting factor for Wi-Fi indoor positioning schemes. In this study, the Manhattan distance was used in the weighted K-nearest neighbour (WKNN) algorithm to improve positioning accuracy. Reference point (RP) intervals were optimised to reduce the complexity of the system. Specifically, two new positioning schemes are proposed in this paper. Scheme 1 uses the cellular network to refine the fingerprint database, while Scheme 2 uses the cellular network positioning to locate the node a priori, then uses the Wi-Fi network to further improve accuracy. The experimental results showed that the average positioning error of Scheme 1 was 1·60 m, a reduction of 12% compared with the existing Wi-Fi fingerprinting schemes. In Scheme 2, when double cellular networks were used, RP usage was reduced by 64% and the calculating time was 0·24 s, a reduction of up to 69·5% compared with the Manhattan-WKNN algorithm. These proposed schemes are suitable for high accuracy and real-time positioning situations, respectively.

In a waist-worn Pedestrian Navigation System (PNS) based on Dead-Reckoning (DR), heading drift caused by Micro-Electro-Mechanical System (MEMS) gyro bias is an essential factor affecting DR accuracy. Considering the characteristics of pedestrian navigation and the poor bias repeatability of MEMS gyros, this paper presents a standing calibration method for MEMS gyro bias. The current gyro biases for each boot can be calibrated accurately in the initial stage before walking. Since the attitude angles calculated by the output data from magnetic sensor and accelerometers do not drift, this paper applies the reverse algorithm of attitude updating to calculate the angular velocities of human motion. Then the gyro biases at each moment can be acquired by subtraction operation between the measured angular velocities from gyros and the calculated angular velocities of human motion. Finally, in order to restrain the random error caused by sensor noise, the calculated biases in the initial stage are smoothed, and consequently the optimal estimate of current gyro biases after each boot can be obtained. Still and dynamic turntable experiments and a walking experiment are performed to compare and analyse the proposed method and the Zero Angular Rate Update (ZARU) method. Experimental results show that the proposed method can also calibrate the gyro bias accurately in the case of body swaying.

This paper proposes an algorithm for the initial alignment method for rocket navigation systems. It uses the inertial freezing alignment to resolve the attitude matrix with respect to its fast and robust characteristics. Due to disturbances from the swaying base environment, such as people walking and wind effect, which would consequently result in a great lever arm effect, a Finite Impulse Response (FIR) filter is utilized to decrease the noise in the accelerometers' measurement. In addition, there are sensor errors in the system; the online estimation of gyroscopes' drift with a Kalman filter is adopted to achieve compensation. Numerical results from a simulated rocket initial alignment experiment are reported to demonstrate the effectiveness of the method.

Based on the candidate architectures of the libration point satellite navigation system proposed in our previous work, a navigation performance study is conducted in this paper to verify the cislunar navigation ability of the proposed system. Using scalar satellite-to-satellite range measurement between the user and libration point navigation satellites, a virtual lunar exploration mission scenario is developed to verify the navigation performance of the candidate Earth-Moon L1,2,4,5 four-satellite constellations. The simulation results indicate that the libration point satellite navigation system is available for cislunar navigation and the navigation accuracy of a few tens of metres can be achieved for both the trans-lunar cruise and lunar orbit phase. Besides that, it is also found that the navigation accuracy of the libration point satellite navigation system is sensitive to the orbit of the L1 satellite. Once the L1 navigation satellite is located in the Halo orbit or vertical Lyapunov orbit, the proposed system can present a better navigation performance in cislunar space.

In this study, we develop a Multi-constellation Global Navigation Satellite System (GNSS) Receiver Differential Code Bias (MGR-DCB) model. The model estimates the receiver DCBs for the Global Positioning System (GPS), BeiDou and Galileo signals from the ionosphere-corrected geometry-free linear combinations of the code observations. In order to account for the ionospheric delay, a Regional Ionospheric Model (RIM) over Europe is developed. GPS observations from 60 International GNSS Servoce (IGS) and EUREF reference stations are processed in the Bernese-5·2 Precise Point Positioning (PPP) module to estimate the Vertical Total Electron Content (VTEC). The RIM has spatial and temporal resolutions of 1° × 1° and 15 minutes, respectively. The receiver DCBs for three stations from the International GNSS Service Multi-GNSS Experiment (IGS-MGEX) are estimated for three different days. The estimated DCBs are compared with the MGEX published values. The results show agreement with the MGEX values with mean difference and Root Mean Square Error (RMSE) values less than 1 ns. In addition, the combined GPS, BeiDou and Galileo VTEC values are evaluated and compared with the IGS Global Ionospheric Maps (IGS-GIM) counterparts. The results show agreement with the GIM values with mean difference and RMSE values less than 1 Total Electron Content Unit (TECU).