Fine initial alignment is vital to the Inertial Navigation System (INS) before the launching of a missile. The existing initial alignment methods are mainly performed on a stationary base after the missile has been erected to the vertical state. However, these methods consume extra alignment time and some state variables have poor degrees of observability, thus losing the rapidity of alignment. In order to solve the problem, a fast fine initial self-alignment method of a missile-borne INS is proposed, which is performed during the erecting process on a stationary base. The convected Euler angle error is modelled to optimise the erecting manoeuvre which can prevent large Euler angle errors and improve the system observability. The fine initial alignment model is established to estimate and correct the initial misalignment. Several experiments verify that the proposed method is effective for improving the rapidity of the fine initial alignment for a missile-borne INS.

Unlike industrial-grade Inertial Navigation Sensors (INSs) that can provide credible tracking performance, more affordable consumer-grade low-cost INSs produce drifts in heading angles and positions that result in a poor tracking accuracy. Researchers have proposed drift correction methods that attempt to attenuate the drifts when walking straight along the dominant directions is detected. While determining the type of a pedestrian's walk is essential before the heading corrections are made, the current detection techniques heavily rely on thresholding. This paper proposes a novel threshold-less method to detect turns in walking by using pelvic rotation and correct the heading angle based on consumer-grade INSs. The experiments indicate the proposed turn detector and heading correction methods produce very good results which can be applied for future pedestrian tracking, activity recognition or rehabilitation.

Vessel behaviour analysis plays an important role in maritime situational awareness. However, available technology still provides only limited approaches to vessel behaviour analysis. In this paper, we propose a visual analytics framework to interactively explore the characteristics of vessel behaviour by means of integrating visualisation with data mining and a human-computer interaction controlling model, which combines human insight with the enormous storage and processing capacities of computers to gain insight into vessel behaviour. In addition, we provide multiple views for visually analysing vessel trajectories, densities and speeds. Case studies with 15 days' AIS data collected from the middle Hankou channel to Yangluo channel in the Yangtze River demonstrate the effectiveness of our approach.

Increasing the stability and reliability of navigation for mobile objects of different classes is becoming increasingly significant. Satellite navigation systems have a fundamental defect: a vulnerability to hacking and spoofing. Observation of the horizon line is significant for two applications. The first is stellar inertial navigation systems. In this case, the horizon line can be used for local vertical estimation. Errors in local vertical estimation directly affect coordinate errors. The second is correlation-extremal navigation based on the observed horizon line shape (when islands or continents are observed from aerial vehicles). In both cases, instability of the horizon line produces navigation errors. A measurement procedure for horizon line position estimation was proposed and realised. Around-the-clock horizon line shooting was undertaken in 2013. Processing of the results shows a horizon line direction instability of about 5–7 angular minutes during the day time.

The acquisition of signals is a precondition for tracking and solution calculation in software-based Global Navigation Satellite System (GNSS) receivers. The Parallel Code phase Acquisition (PCA) algorithm can simultaneously obtain the correlation results at every sampling point. However, if the number of sampling points that needs processing is large, this method will lead to a heavy computational load. Thus, we improve the process of the PCA algorithm and propose a novel algorithm that divides the signals into K (K is a constant) parts to achieve correlation and obtains the correlation results with a fusion algorithm. This algorithm can simultaneously obtain the correlation results for sampling points at an interval of K points. If the K value is selected appropriately, the computational load can be decreased by about 50%. Also, the Receiver Operating Characteristic (ROC) curves show that under a certain probability of false alarm, the detection probability of the proposed algorithms is 5% lower than that of the PCA algorithm. Therefore, the proposed algorithm can speed up the acquisition process with a slight decrease in detection probability.

Since the descriptors based on Three-Dimensional (3D) Zernike moments are robust to geometric transformations and noise, they have been proposed for terrain matching. However, terrain matching algorithms based on 3D Zernike Moments (3DZMs) are often difficult to implement in practice since they are computationally intensive. This paper presents a more efficient real-time terrain matching algorithm based on 3DZMs for land applications. Two efficient methods based on coordinate transformation and symmetry are proposed to compute the geometric moments. The impact of the sample difference on the matching result due to heading angle is investigated to prove the feasibility of using a circular template. Consequently, the terrain feature vectors of the reference map can be computed off-line with the circular template to significantly reduce on-line computation. Numerical experiments on a real digital elevation model demonstrate that the proposed algorithm is robust to the heading angle and can be implemented for real-time terrain matching operations.

Motion compensation is a significant part of an airborne remote sensing system. A Position and Orientation System (POS) can directly measure the motion information of an airborne remote sensing payload that can improve the quality of airborne remote sensing images. Gravity disturbance, information on which is often ignored due to being difficult to acquire in real-time, has become the main error source of POS in the development of inertial components. In this paper, a new real-time gravity compensation method is proposed, which includes the gravity disturbance as the error states of a POS Kalman filter, and an accurate gravity disturbance model is constructed using a time-varying Gaussian-Markov model based on a high-precision gravity map, whose resolution is enhanced by a new interpolation method based on Gaussian Process Regression (GPR). A flight experiment was conducted to evaluate the efficiency of the proposed method and the results showed that the proposed method performs well when compared with other real-time gravity compensation methods.

The basis of all recommended methods for obtaining position by using celestial bodies is the known altitude of the celestial body being observed. Accordingly, it is necessary to have a sextant, classic or with an artificial horizon, or some other device that can measure altitude. However, there is a way to obtain position using astronomical navigation without determining the altitude of a celestial body, and this method will be analysed in this paper. The introduced method requires only precise measurement of the azimuth, and is based on determining two positions close to the dead reckoning position and lying on the isoazimuthal curve, i.e. a curve of the same great circle azimuths of a celestial body. Furthermore, the model assumes that a part of this curve, between the selected positions, can be replaced by a straight line. Special attention will be given to the analysis of errors of the line of position for various azimuth errors and various dead reckoning (assumed) positions. It will also be shown how a modern Electronic Chart Display and Information System (ECDIS) can help in approximate position determination, knowing only the azimuths of celestial bodies.

As Satellite Clock Bias (SCB) prediction may be affected by various factors such as periodic items, sampling length, and stochastic items, a fusion-based prediction method is proposed by considering characteristics of SCB and fitted residue. On this basis, an instance algorithm is presented by fusing four typical prediction models. First, we use Empirical Mode Decomposition (EMD) to pre-process and decompose the SCB series into multiple components with various characteristics. Then, we analyse the fitting performance of each model for different components and prediction length, namely short-, mid- and long-term prediction, and select models with the best performance. Next, we analyse fitted residue of the reconstructed SCB, and select the model with the best fitting results. Finally, we fuse the multiple selected models for SCB prediction. The method is tested using Global Positioning System (GPS) precise clock products provided by the International Global Navigation Satellite System Service (IGS). Experimental results show that, compared with single prediction models and existing combination models, the proposed fusion-based prediction method improves accuracy and stability. In particular, the proposed method is more stable and has better performance for mid- and long-term prediction.

As the geographical meridians converge rapidly, traditional inertial navigation methods fail in the polar regions. Classic transversal navigation methods can address the problem by transversal rotation of the original north and south poles, but this can introduce errors based on the spherical Earth model. To reduce the principle errors, some fruitful research work using an ellipsoidal Earth model has been done. Under the ellipsoid Earth model, transversal navigation for polar region becomes a complex coupling problem. Considering the coupling of the three-dimensional motion, a more rigorous mechanism for transversal navigation using an ellipsoidal Earth model is proposed. Starting from the relationship between Euclidean coordinates and spherical coordinates, the main equations of transversal polar navigation based on an ellipsoidal Earth model are derived in detail. Complete mechanical arrangements of attitude, position and velocity calculation are presented. The new derivation in this paper completely avoids solving the ellipsoidal radius. Numerical results indicate that the proposed transversal navigation mechanism can outperform the traditional method, especially in the condition of vertical motion.

For underwater vehicle navigation sensors, the output signal periods are different and time-varying. This would result in the decline of precision, and even wrong results. To deal with the problem, this paper puts forward a multi-sensor, adjustable-period integrated navigation method based on multi-stage signal trigger. This method considers the valid signals of a Doppler Velocity Log (DVL) as the trigger signals of a Dead-Reckoning (DR) navigation program. It also considers the valid signals of an acoustic positioning sensor as the trigger signals of the integrated navigation program. In this method, it can adjust the filtering period in real time. According to the time label of signals, this method actualises the time-space alignment of sensors. Then it conducts DR navigation and integrated navigation. The method can not only utilise the valid signals of each sensor sufficiently but also fuses the data based on time-space alignment efficiently. Sea trial data shows that when the output signal periods are certain, navigation precision of the method in this paper is better than a non-adjustable-period filtering method. Moreover, in poor conditions, it can also attain a high precision.

Data derived from the Automatic Identification System (AIS) plays a key role in water traffic data mining. However, there are various errors regarding time and space. To improve availability, AIS data quality dimensions are presented for detecting errors of AIS tracks including physical integrity, spatial logical integrity and time accuracy. After systematic summary and analysis, algorithms for error pre-processing are proposed. Track comparison maps and traffic density maps for different types of ships are derived to verify applicability based on the AIS data from the Chinese Zhoushan Islands from January to February 2015. The results indicate that the algorithms can effectively improve the quality of AIS trajectories.

A novel synthetic air data estimation method without using air data sensors is presented, and the method only relies on the information from the Navigation System (NS) and Flight Control System (FCS). The aircraft's aerodynamic model is also required to make a connection between the FCS control parameters and the NS measurements. The airspeed, angle of attack and sideslip, angular velocity and wind speed are defined as state vectors, and state equations are established through the aircraft's aerodynamic model and dynamics. Linear velocity and angular velocity provided by the navigation system are considered as the measurement vector. To deal with variable wind fields, a novel Initialised Three-step Extended Kalman Filter (ITEKF), which considers the wind speed as an unknown input, is developed to track the variation of wind speed. Simulation results based on a Generic Hypersonic Vehicle (GHV) model are presented and compared with an existing method. Factors affecting the method's accuracy include the navigation system accuracy and the aerodynamic model error, are also discussed.

The Micro-Nano satellite TianTuo-3 (TT-3) developed by the National University of Defense Technology (NUDT) was successfully launched on 20 September 2015. The space-based Automatic Identification System (AIS) on board TT-3 works well and stably receives AIS signals from global vessels. In this work, we perform statistical analysis on the detection probability of the vessels in the concerned areas by using the TT-3 AIS data. The results suggest that the detection probability of vessels decreases as the distribution density increases, especially in the offshore areas of dense traffic and the TT3-AIS vessel detection probability in the oceans can be higher than 40%, indicating that the TT-3 AIS has achieved a high probability of coverage of vessels for a single receiving antenna. The analysis results will present helpful references both in evaluating the potential application of satellite-based AIS and for designing the next generation space-based AIS which might greatly improve the detection probability of ocean-going vessels.

Approaching the problem from the internal factors and in particular the inherent state model of a Kalman Filter, this paper presents a novel Strapdown Inertial Navigation System (SINS) modelling, which is obtained with a pseudo-north-oriented mechanisation in a pseudo-geographic frame. Improved modelling associated with the backward algorithm is proposed to achieve velocity-aided in-motion alignment. Compared with traditional algorithms, the proposed method can eliminate the influence of alignment model on the performance of initial alignment caused by SINS modelling. On the other hand, the backward process can still be used to accelerate the process of alignment. As a result, the proposed method is expected to assist those methods only considered from external factors (such as coarse accuracy, process noise, measurement noise, and so on) to improve the stability and robustness of a velocity-aided in-motion alignment system and to solve the modelling problem of high latitude alignment without sacrificing alignment accuracy. Finally, simulations and field experiments with a navigation-grade SINS demonstrate the superior performance of the proposed method.

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.

The BeiDou navigation satellite system (BDS) has been providing a regional service in the Asia–Pacific area since 27 December 2012, and a new Inclined Geosynchronous Satellite Orbit (IGSO) satellite IGSO-6 joined the 14-satellite constellation in operation on 29 March 2016. In this paper, the signal and positioning performance of IGSO-6 are assessed. Compared with other IGSOs, the carrier-to-noise-density ratios of IGSO-6 show comparable performance for the B3 signal and a lower power level for the B2 signal, while the B1 signal is more powerful and has the lowest noise and multipath errors. The satellite-induced code bias of IGSO-6 was investigated and indicates that IGSO-6 has similar characteristics to other IGSOs. The different inter-frequency bias variations among IGSOs with daily periodicity are demonstrated. The BDS positioning performances with IGSO-6 were investigated in Single Point Positioning (SPP) and Precise Point Positioning (PPP) modes at the 95% confidence level. For SPP, there was an improvement of about 4·9% and 3·6% in the horizontal and vertical components, respectively. The convergence time was improved by about 18·3% and 17·8% in the horizontal and vertical components for positioning accuracy to be better than 50 cm, respectively.

A novel fast adaptive-gain complementary filter algorithm is developed for Unmanned Aerial Vehicle (UAV) attitude estimation. This approach provides an accurate, robust and simple method for attitude estimation with minimised attitude errors and reduced computation. UAV attitude data retrieved from accelerometer data is transformed to the solution of a linearly discrete dynamic system. A novel complementary filter is designed to fuse accelerometer and gyroscope data, with a self-adjusted gain to achieve a good performance in accuracy. The performance of the proposed algorithm is compared with an Adaptive-gain Complementary Filter (ACF) and Extended Kalman Filtering (EKF). Simulation and experimental results show that the accuracy of the proposed filter has the same performance as an EKF in high dynamic operating conditions. Therefore, the proposed algorithm can balance accuracy and time consumption, and it has a better price/performance ratio in engineering applications.

Heading angle is a vital parameter in maintaining a vessel's track along a planned course and should be guaranteed in a stable and reliable way. An innovative method of heading determination based on a fisheye camera, which is almost totally unaffected by electromagnetism and geomagnetism, is proposed in this paper. In addition, unlike traditional astronomical methods, it also has a certain degree of adaptability to cloudy weather. Utilising the super wide Field Of View (FOV) of the camera, it is able to simultaneously image the Moon and the horizon. The Moon is treated as the observed celestial body and the horizon works as the horizontal datum. Two experiments were conducted at sea, successfully proving the feasibility of this method. The proposed heading determination system has the merits of automation, resistance to interference and could be miniaturised, making application viable.