The robust parameter estimation of unknown space objects is essential to the on-orbit servicing missions. Based on the adaptive filtering techniques along with the dual quaternions modeling methods for pose estimation, this article proposes a dual vector quaternions-based extended Kalman filter and a dual vector quaternions-based adaptive fading factors extended Kalman filter to estimate the parameters of a free-floating tumbling space target. Using the dual vector quaternions to model the kinematics and dynamics of the system, the representation of the model is concise and compact. Also, the translational and rotational coupled effects are considered. In addition, the estimation algorithm is designed by the innovation-based multiple adaptive fading factors. As a result, the dual vector quaternions-based adaptive fading factors extended Kalman filter is robust against the faulty measurements which may lead to divergence of the traditional extended Kalman filter. As far as the authors know, both the designed filters are the first pose and inertial parameters estimation algorithms based on dual vector quaternions, and the dual vector quaternions-based adaptive fading factors extended Kalman filter is the first robust dual vector quaternions-based parameters estimating method. Finally, the proposed dual vector quaternions-based extended Kalman filter and dual vector quaternions-based adaptive fading factors extended Kalman filter are validated by mathematical simulations, and the dual vector quaternions-based adaptive fading factors extended Kalman filter is compared with the dual vector quaternions-based extended Kalman filter to show its robust performances.

Underwater direction-of-arrival (DOA) tracking using a hydrophone array is an important research subject in passive sonar signal processing. In this study, considering that an unknown underwater environment results in uncertain disturbances to the measurements, robust underwater DOA tracking with regard to uncertain environmental disturbances was studied. Because the uniform circular array (UCA) is free from the port and starboard ambiguity problem, a UCA was used to obtain the measurements for a long-time tracking scenario. First, a kinematic model of an underwater target and a measurement model based on the received signal of the UCA were established. Then, a DOA tracking algorithm was derived based on the extended Kalman filter (EKF), whose performance is significantly affected by the accuracy of the measurement noise covariance matrix (MNCM). Finally, considering that uncertain disturbances carry out unstable measurement noise, the modified Sage–Husa algorithm was used to obtain accurate MNCMs during the process of the derived EKF-based DOA tracking algorithm. Thus, a robust DOA tracking method with uncertain environmental disturbances using a UCA was proposed. The accuracy and reliability of the suggested method was verified via Monte Carlo simulations of a DOA tracking scenario and an experiment in the South China Sea in July 2021.

Estimating the parameters of an unknown free-floating tumbling spacecraft is an essential task for the on-orbit servicing missions. This paper proposes a dual vector quaternion based fault-tolerant pose and inertial parameters estimation algorithm of an uncooperative space target using two formation flying small satellites. Firstly, by utilizing the dual vector quaternions to model the kinematics and dynamics of the system, not only the representation of the model is concise and compacted, but also the translational and rotational coupled effects are considered. By using this modeling technique along with the measurements from the on-board vision-based sensors, a dual vector quaternion based extended Kalman filter for each of the two small satellites is designed. Secondly, both of the estimations from each small satellite will be used as inputs of the fault-tolerant algorithm. This algorithm is based on the fault-tolerant federal extended Kalman filter strategy to overcome the estimation errors caused by the faulty measurements, the unknown space environment and the computing errors by setting the appropriate ratios of the two estimations from the first step dual vector quaternions extended Kalman filter. Together with the first and second steps, a novel fault-tolerant dual vector quaternions federal extended Kalman filter using two formation flying small satellites is proposed by this paper to estimate the pose and inertial parameters of a free-floating tumbling space target. By utilizing the estimation algorithm, a good prior knowledge of the unknown space target can be achieved. Finally, the proposed dual vector quaternion federal extended Kalman filter is validated by mathematical simulations to show its robust performances.

The bearing-only tracking of an underwater uncooperative target can protect maritime territories and allows for the utilization of sea resources. Considering the influences of an unknown underwater environment, this work aimed to estimate 2-D locations and velocities of an underwater target with uncertain underwater disturbances. In this paper, an adaptive two-step bearing-only underwater uncooperative target tracking filter (ATSF) for uncertain underwater disturbances is proposed. Considering the nonlinearities of the target’s kinematics and the bearing-only measurements, in addition to the uncertain noise caused by an unknown underwater environment, the proposed ATSF consists of two major components, namely, an online noise estimator and a robust extended two-step filter. First, using a modified Sage-Husa online noise estimator, the uncertain process and measurement noise are estimated at each tracking step. Then, by adopting an extended state and by using a robust negative matrix-correcting method in conjunction with a regularized Newton-Gauss iteration scheme, the current state of the underwater uncooperative target is estimated. Finally, the proposed ATSF was tested via simulations of a 2-D underwater uncooperative target tracking scenario. The Monte Carlo simulation results demonstrated the reliability and accuracy of the proposed ATSF in bearing-only underwater uncooperative tracking missions.