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Bayesian cubature (BC) has emerged to be one of most competitive approach for estimating the multi-dimensional integral especially when the integrand is expensive to evaluate, and alternative acquisition functions, such as the Posterior Variance Contribution (PVC) function, have been developed for adaptive experiment design of the integration points. However, those sequential design strategies also prevent BC from being implemented in a parallel scheme. Therefore, this paper aims at developing a parallelized adaptive BC method to further improve the computational efficiency.

By theoretically examining the multimodal behavior of the PVC function, it is concluded that the multiple local maxima all have important contribution to the integration accuracy as can be selected as design points, providing a practical way for parallelization of the adaptive BC. Inspired by the above finding, four multimodal optimization algorithms, including one newly developed in this work, are then introduced for finding multiple local maxima of the PVC function in one run, and further for parallel implementation of the adaptive BC.

The superiority of the parallel schemes and the performance of the four multimodal optimization algorithms are then demonstrated and compared with the k-means clustering method by using two numerical benchmarks and two engineering examples.

Multimodal behavior of acquisition function for BC is comprehensively investigated. All the local maxima of the acquisition function contribute to adaptive BC accuracy. Parallelization of adaptive BC is realized with four multimodal optimization methods.

A novel vision-based relative navigation system (VBRNS) plays an important role in aeronautics and astronautics fields, and the filter is the core of VBRNS. However, most of the existing filtering algorithms used in VBRNS are derived based on Gaussian assumption and disregard the non-Gaussianity of VBRNS. Therefore, a novel robust filtering named as cubature Huber-based filtering (CHF) is proposed and applied to VBRNS to improve the navigation accuracy in non-Gaussian noise case.

Under the Bayesian filter framework, the third-degree cubature rule is used to compute the cubature points which are propagated through state equation, and then the predicted mean and the associated covariance are taken. A combined minimum l₁ and l₂-norm estimation method referred as Huber’s criterion is used to design the measurement update. After that, the vision-based relative navigation model is presented and the CHF is used to integrate the line-of-sight measurements from vision camera with inertial measurement of the follower to estimate the precise relative position, velocity and attitude between two unmanned aerial vehicles. During the design of relative navigation filter, the quaternions are used to represent the attitude and the generalized Rodrigues parameters are used to represent the attitude error. The simulation is conducted to demonstrate the effectiveness of the algorithm.

By this means, the VBRNS could perform better than traditional VBRNS whose filter is designed by Gaussian filtering algorithms. And the simulation results demonstrate that the CHF could exhibit robustness when the system is non-Gaussian. Moreover, the CHF has more accurate estimation and faster rate of convergence than extended Kalman Filtering (EKF) in face of inaccurate initial conditions.

A novel robust nonlinear filtering algorithm named as CHF is proposed and applied to VBRNS based on cubature Kalman filtering (CKF) and Huber’s technique. The CHF could adapt to the non-Gaussian system effectively and perform better than traditional Gaussian filtering such as EKF.

The sensorless external force estimation of robot manipulator can be helpful for reducing the cost and complexity of the robot system. However, the complex friction phenomenon of the robot joint and uncertainty of robot model and signal noise significantly decrease the estimation accuracy. This study aims to investigate the friction modeling and the noise rejection of the external force estimation.

A LuGre-linear-hybrid (LuGre-L) friction model that combines the dynamic friction characteristics of the robot joint and static friction of the drive motor is proposed to improve the modeling accuracy of robot friction. The square root cubature Kalman filter (SCKF) is improved by integrating a Sage Window outer layer and a nonlinear disturbance observer (NDOB) inner layer. In the outer layer, Sage Window is integrated in the square root Kalman filter (W-SCKF) to dynamically adjust noise statistics. NDOB is applied as the inner layer of W-SCKF (NDOB-WSCKF) to obtain the uncertain state variables of the state model.

A peg-in-hole contact experiment conducted on a real robot demonstrates that the average accuracy of the estimated joint torque based on LuGre-L is improved by 4.9% in contrast to the LuGre model. Based on the proposed NDOB-WSCKF, the average estimation accuracy of the external joint torque can reach up to 92.1%, which is improved by 4%–15.3% in contrast to other estimation methods (SCKF and NDOB).

A LuGre-L friction model is proposed to handle the coupling of static and dynamic friction characteristics for the robot manipulator. An improved SCKF is applied to estimate the external force of the robot manipulator. To improve the noise rejection ability of the estimation method and make it more resistant to unmodeled state variable, SCKF is improved by integrating a Sage Window and NDOB, and a NDOB-WSCKF external force estimator is developed. Validation results demonstrate that the accuracy of the robot dynamics model and the estimated external force is improved by the proposed method.

The purpose of this study is to establish an effective tracking algorithm for small unmanned aerial vehicles (UAVs) based on interacting multiple model (IMM) to take timely countermeasures against illegal flying UAVs.

In this paper, based on the constant velocity model (CV), the maneuvering adaptive current statistical model (CS) and the angular velocity adaptive three-dimensional (3D) fixed center constant speed rate constant steering rate model, a small UAV tracking algorithm based on adaptive interacting multiple model (AIMM-UKF) is proposed. In addition, an adaptive robust filter is added to each model of the algorithm. The linear Kalman filter algorithm is attached to the CV model and the CS model and the unscented Kalman filter algorithm (UKF) is attached to the CSCDR model to solve the nonlinearity of the 3D turning model.

Monte-Carlo simulation comparison with the other two IMM tracking algorithms shows that in the case of different movement modes and maneuvering strength of the UAV, the AIMM-UKF algorithm makes a good trade-off between the amount of calculation and filtering accuracy, which can maintain more accurate and stable tracking and has strong robustness. At the same time, after testing the actual observation data of the UAV, the results show that the AIMM-UKF algorithm state estimation trajectory can be regarded as an actual trajectory in practical engineering applications, which has good practical value.

This paper presents a new small UAV tracking algorithm based on IMM and the advantages and practicability of this algorithm compared with existing algorithms are proved through experiments.

Doppler-Bearing Tracking (DBT) is commonly used in target tracking applications for the underwater environment using the Hull-Mounted Sensor (HMS). It is an important and challenging problem in an underwater environment.

The system nonlinearity in an underwater environment increases due to several reasons such as the type of measurements taken, the speeds of target and observer, environmental conditions, number of sensors considered for measurements and so on. Degrees of nonlinearity (DoNL) for these problems are analyzed using a proposed measure of nonlinearity (MoNL) for state estimation.

In this research, the authors analyzed MoNL for state estimation and computed the conditional MoNL (normalized) using different filtering algorithms where measurements are obtained from a single sensor array (i.e. HMS). MoNL is implemented to find out the system nonlinearity for different filtering algorithms and identified how much nonlinear the system is, that is, to measure nonlinearity of a problem.

Algorithms are evaluated for various scenarios with different angles on the target bow (ATB) in Monte-Carlo simulation. Computation of root mean squared (RMS) errors in position and velocity is carried out to assess the state estimation accuracy using MATLAB.

From many decades, bearings-only tracking (BOT) is the interested problem for researchers. This utilises nonlinear filtering methods for state estimation as there is only information about the target, i.e. bearing is a nonlinear measurement. The measurement bearing is tangentially related to the target state vector. There are many nonlinear filtering algorithms developed so far in the literature.

In this research work, the recently developed nonlinear filtering algorithm, i.e. shifted Rayleigh filter (SRF), is applied to BOT.

The SRF is tested for two-dimensional BOT against various scenarios. The simulation results emphasise that the SRF performs well when compared to the standard nonlinear filtering algorithm, unscented Kalman filter (UKF).

SRF utilises the nonlinearities present in the bearing measurement through the use of moment matching. The SRF is able to produce the solution in highly noisy environment, long ranges and high dimension tracking.

The successful use of the standard extended Kalman filter (EKF) is restricted by the requirement on the statistics information of the measurement noise. The covariance of the measurement noise may deviate from its nominal value in practical environment, and the filtering performance may decline because of the statistical uncertainty. Although the adaptive EKF (AEKF) is available for recursive covariance estimation, it is often less accurate than the EKF with accurate noise statistics.

Aiming at this problem, this paper develops a parallel adaptive EKF (PAEKF) by combining the EKF and the AEKF with an adaptive law, such that the final state estimate is dominated by the EKF when the prior noise covariance is accurate, while the AEKF is activated when the actual noise covariance deviates from its nominal value.

The PAEKF can reduce the sensitivity of the algorithm to the model uncertainty and ensure the estimation accuracy in the normal case. The simulation results demonstrate that the PAEKF has the advantage of both the AEKF and the EKF.

The presented algorithm is applicable for spacecraft relative attitude and position estimation.

The PAEKF is presented for a kind of nonlinear uncertain systems. Stability analysis is provided to show that the error of the estimator is bounded under certain assumptions.

For autonomous vehicles, trajectory prediction of surrounding vehicles is beneficial to improving the situational awareness of dynamic and stochastic traffic environments, which is a crucial and indispensable element to realize highly automated driving.

In this paper, the overall framework consists of two parts: first, a novel driver characteristic and intention estimation (DCIE) model is built to indicate the higher-level information of the vehicle using its low-level motion variables; then, according to the estimation results of the DCIE model, a classified Gaussian process model is established for probabilistic vehicle trajectory prediction under different motion patterns.

The whole method is later applied and analyzed in the highway lane-change scenarios with the parameters of models learned from the public naturalistic driving data set. Compared with other traditional methods, the performance of this proposed approach is proved superior, demonstrated by the higher accuracy in the long prediction horizon and a more reasonable description of uncertainty.

This hierarchical approach is proposed to make trajectory prediction accurately both in the short term and long term, which can also deal with the uncertainties caused by the perception system or indeterminate vehicle behaviors.