In normal working conditions it is possible to achieve sufficient attitude estimation accuracy for a satellite using regular Kalman filter algorithm. On the other hand, when there is a fault in the measurements, the Kalman filter fails in providing the required accuracy and may even collapse over time. In this paper, a Robust Kalman filtering method is proposed for the attitude estimation probl...

| Modeling a noisy time series requires the dual estimation of both the model parameters and the underlying clean time series. Most approaches estimate the model parameters by minimizing the mean squared prediction error, but estimate the time series by minimizing another cost function. We justify the use of the same maximum-likelihood cost for both parameter and time series estimation, and pre...

For long memory time series models with uncorrelated but dependent errors, we establish the asymptotic normality of the Whittle estimator under mild conditions. Our framework includes the widely used FARIMA models with GARCH-type innovations. To cover nonstationary fractionally integrated processes, we extend the idea of Abadir, Distaso and Giraitis (2007, Journal of Econometrics 141, 13531384)...

A biochemical dynamic pathway is usually modeled as a nonlinear system described by a set of nonlinear ODEs. In most cases, only partial states can be measured. Moreover, the system parameters, reaction rates, may be unknown or poorly known. Therefore, it is of significance to estimate the states and parameters, for analyzing the biochemical dynamic pathway. Due to the limitation of some tradit...

We present a new motion estimation framework and apply it to omni-directional imagery. Our method estimates motions incrementally using an Implicit Extended Kalman Filter (IEKF). Each individual feature provides partial information about the camera motion. The motion estimate is incrementally improved as each feature is processed, similar to the SCAAT approach. The SCAAT method was developed fo...

Image splicing detection is of fundamental importance in digital forensics and therefore has attracted increasing attention recently. In this paper, a color image splicing detection approach is proposed based on Markov transition probability of quaternion component separation in quaternion discrete cosine transform (QDCT) domain and quaternion wavelet transform (QWT) domain. Firstly, Markov fea...

We develop a quaternion wavelet transform (QWT) as a new multiscale analysis tool for geometric image features. The QWT is a near shift-invariant, tight frame representation whose coefficients sport a magnitude and three phase values, two of which are directly proportional to local image shifts. The QWT can be efficiently computed using a dual-tree filter bank and is based on a 2-D Hilbert tran...

The absolute orientation problem has applications in numerous fields; including robotics, pose estimation, photogrammetry, and computer graphics. With the exception of the contributions by B. K. P. Horn, most absolute orientation research has focused on rotation matrixes. However, in many cases, representing rotations as quaternions has significant advantages over the more traditional forms. Th...

The performances of three attitude determination algorithms are compared in this paper. The three methods are the Complementary Filter, a Quaternion-based Kalman Filter and a Quaternion-based Gradient Descent Algorithm. An analysis of their performance based on an experimental investigation was undertaken. This paper shows that the Complementary Filter requires the least computational power; Qu...

Various attitude estimation methods are based on an optimization problem posed in 1965 by Grace Wahba, which is called Wahba’s the field of estimation. As a key for determination, many different algorithms minimizing loss function have been proposed past 60 years. Among most representative Quaternion Estimator (QUEST), Singular Value Decomposition (SVD), and Fast Optimal Attitude Matrix (FOAM),...