This paper presents a robust train localisation system by fusing a Global Navigation Satellite System (GNSS) with an Inertial Navigation System (INS) in a tightly-coupled (TC) strategy. To improve navigation performance in GNSS partly blocked areas, an advanced map-matching (MM) measurement-augmented TC GNSS/INS method is proposed via an error-state unscented Kalman filter (UKF). The advanced MM generates a matched position using a one-step predicted position from a UKF time update step with binary search algorithm and a point–line projection algorithm. The matched position inputs as an additional measurement to fuse with the INS position to augment the degraded GNSS pseudorange measurement to optimise the state estimation in the UKF measurement update step. Both the real train test on the Qinghai–Tibet railway and the simulation were carried out and the results confirm that the proposed advanced MM measurement-augmented TC GNSS/INS with error-state UKF provides the best horizontal positioning accuracy of 0 ⋅ 67 m, which performs an improvement of about 71% and 90% with respect to TC GNSS/INS with only error-state UKF and only error-state Extended Kalman filter in GNSS partly blocked areas.

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.

It is well known that the presence of outliers can mis-estimate (underestimate or overestimate) the overall reserve in the chain-ladder method, when we consider a linear regression model, based on the assumption that the coefficients are fixed and identical from one observation to another. By relaxing the usual regression assumptions and applying a regression with randomly varying coefficients, we have a similar phenomenon, i.e., mis-estimation of the overall reserves. The lack of robustness of loss reserving regression with random coefficients on incremental payment estimators leads to the development of this paper, aiming to apply robust statistical procedures to the loss reserving estimation when regression coefficients are random. Numerical results of the proposed method are illustrated and compared with the results that were obtained by linear regression with fixed coefficients.

The primary objective of this scholarly work is to develop two estimation procedures – maximum likelihood estimator (MLE) and method of trimmed moments (MTM) – for the mean and variance of lognormal insurance payment severity data sets affected by different loss control mechanism, for example, truncation (due to deductibles), censoring (due to policy limits), and scaling (due to coinsurance proportions), in insurance and financial industries. Maximum likelihood estimating equations for both payment-per-payment and payment-per-loss data sets are derived which can be solved readily by any existing iterative numerical methods. The asymptotic distributions of those estimators are established via Fisher information matrices. Further, with a goal of balancing efficiency and robustness and to remove point masses at certain data points, we develop a dynamic MTM estimation procedures for lognormal claim severity models for the above-mentioned transformed data scenarios. The asymptotic distributional properties and the comparison with the corresponding MLEs of those MTM estimators are established along with extensive simulation studies. Purely for illustrative purpose, numerical examples for 1500 US indemnity losses are provided which illustrate the practical performance of the established results in this paper.

Real-time and accurate fault detection and isolation is very important to ensure the reliability and precision of integrated inertial navigation and global navigation satellite systems. In this paper, the detection performance of a residual chi-square method is analysed, and on this basis an improved method of fault detection is proposed. The local test based on a standardised residual is introduced to detect and identify faulty measurements directly. Differing from the traditional method, two appropriate thresholds are selected to calculate the weight factor of each measurement, and the gain matrix is adjusted adaptively to reduce the influence of the undetected faulty measurement. The sliding window test, which uses past measurements, is also added to further improve the fault detection performance for small faults when the local test based on current measurements cannot judge whether a fault has occurred or not. Several simulations are conducted to evaluate the proposed method. The results show that the improved method has better fault detection performance than the traditional detection method, especially for small faults, and can improve the reliability and precision of the navigation system effectively.

This paper discusses the estimation algorithms for Three-Dimensional (3D) displacement and 3D rotation using Two-Dimensional (2D) laser scanners. An efficient outlier detection method is proposed for both algorithms to help protect the integrity of navigation. The algorithms have been evaluated using both simulation and field test results. They are able to produce a robust odometry solution for an autonomous aircraft in an indoor environment.

This paper proposes the novel use of a weighted Interval Kalman Filter (wIKF) in a robust navigational approach for integration with the guidance and control systems of an uninhabited surface vehicle named Springer. The waypoint tracking capability of this technique is compared with that of one that uses a conventional Kalman Filter (KF) navigational design, when the model of the sensing equipment used by the filter is incorrect. In this case, the KF fails to predict correctly the vehicle's heading, which consequently impacts negatively on the performance of its integrated navigation, guidance and control (NGC). However, the use of a wIKF technique that is immune to this kind of erroneous modelling endows the integrated NGC system with better accuracy and efficiency in completing a mission.

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.

Integrated navigation using multiple Global Navigation Satellite Systems (GNSS) is beneficial to increase the number of observable satellites, alleviate the effects of systematic errors and improve the accuracy of positioning, navigation and timing (PNT). When multiple constellations and multiple frequency measurements are employed, the functional and stochastic models as well as the estimation principle for PNT may be different. Therefore, the commonly used definition of “dilution of precision (DOP)” based on the least squares (LS) estimation and unified functional and stochastic models will be not applicable anymore. In this paper, three types of generalised DOPs are defined. The first type of generalised DOP is based on the error influence function (IF) of pseudo-ranges that reflects the geometry strength of the measurements, error magnitude and the estimation risk criteria. When the least squares estimation is used, the first type of generalised DOP is identical to the one commonly used. In order to define the first type of generalised DOP, an IF of signal–in-space (SIS) errors on the parameter estimates of PNT is derived. The second type of generalised DOP is defined based on the functional model with additional systematic parameters induced by the compatibility and interoperability problems among different GNSS systems. The third type of generalised DOP is defined based on Bayesian estimation in which the a priori information of the model parameters is taken into account. This is suitable for evaluating the precision of kinematic positioning or navigation. Different types of generalised DOPs are suitable for different PNT scenarios and an example for the calculation of these DOPs for multi-GNSS systems including GPS, GLONASS, Compass and Galileo is given. New observation equations of Compass and GLONASS that may contain additional parameters for interoperability are specifically investigated. It shows that if the interoperability of multi-GNSS is not fulfilled, the increased number of satellites will not significantly reduce the generalised DOP value. Furthermore, the outlying measurements will not change the original DOP, but will change the first type of generalised DOP which includes a robust error IF. A priori information of the model parameters will also reduce the DOP.

In the last decades, robust estimation has been widely applied to overcome the presence of gross errors in observations. Recently it has been shown that robust estimation, if computed appropriately, is able to cope with a larger amount of gross errors and also capable of providing reliable estimations in situations where systematic errors are present. It is the purpose of this paper to propose the use of global robust estimation for computing baselines strongly affected by multipath effects.

In this paper a brief review of Sage adaptive filtering is followed by an analysis of the shortcomings of covariance matrices formed by windowing residual vectors, innovation vectors and correction vectors of the dynamic states. A new adaptive Kalman filter is developed by combining the Sage filter and the variance components and its use tested against various other schemes.

The standard linear regression model is analysed using a method called functional least squares which yields a family of estimators for the slope parameter indexed by a real variable t, |t| ≦ T. The choice t = 0 corresponds to ordinary least squares, non-zero values being appropriate if the error distribution is long-tailed, and it is argued that the approach is a natural extension of least squares methodology. It emerges that the asymptotic normal distribution of these estimators has a covariance matrix characterised by a scalar function of t, called the variance function, which is determined by the error distribution. Properties of this variance function suggest graphical criteria for detecting departures from normality.