Determination of relative three-dimensional （3D） position, orientation, and relative motion between two reference frames is an important problem in robotic guidance, manipulation, and assembly as well as in other fields such as photogrammetry. A solution to pose and motion estimation problem that uses two-dimensional （2D） intensity images from a single camera is desirable for real-time applications. The difficulty in performing this measurement is that the process of projecting 3D object features to 2D images is a nonlinear transformation. In this paper, the 3D transformation is modeled as a nonlinear stochastic system with the state estimation providing six degrees-of-freedom motion and position values, using line features in image plane as measuring inputs and dual quaternion to represent both rotation and translation in a unified notation. A filtering method called the Gaussian particle filter （GPF） based on the panicle filtering concept is presented for 3D pose and motion estimation of a moving target from monocular image sequences. The method has been implemented with simulated data, and simulation results are provided along with comparisons to the extended Kalman filter （EKF） and the unscented Kalman filter （UKF） to show the relative advantages of the GPF. Simulation results showed that GPF is a superior alternative to EKF and UKF.
On the assumption that random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables, this paper generalize the extended Kalman filtering （EKF）, the unscented Kalman filtering （UKF） and the Gaussian particle filtering （GPF） to the case in which there is a positive probability that the observation in each time consists of noise alone and does not contain the chaotic signal （These generalized novel algorithms are referred to as GEKF, GUKF and GGPF correspondingly in this paper）. Using weights and network output of neural networks to constitute state equation and observation equation for chaotic time-series prediction to obtain the linear system state transition equation with continuous update scheme in an online fashion, and the prediction results of chaotic time series represented by the predicted observation value, these proposed novel algorithms are applied to the prediction of Mackey-Glass time-series with additive and multiplicative noises. Simulation results prove that the GGPF provides a relatively better prediction performance in comparison with GEKF and GUKF.
