arXiv subjects

Li Qiao

Publications and source records attributed to Li Qiao.

39 records · Page 3Linked to original sources

arXiv2016

Position and Velocity estimation of Re-entry Vehicles using Fast Unscented Kalman Filters

Application of two new UKF based estimation techniques with reduced processing time in re-entry vehicle position and velocity estimation problem using ground-based range and elevation measurements is presented. The first method is called the Single Propagation Unscented Kalman Filter (SPUKF) where, the a postiriori state is propagated only once and then the sampled sigma points at the next time state are approximated by the first-order Taylor Series terms. In the second method called the Extrapolated Single Propagation Unscented Kalman Filter (ESPUKF), the sigma points are approximated to the second-order Taylor Series terms using the Richardson Extrapolation. The EKF, SPUKF, ESPUKF and the UKF are utilized in a re-entry vehicle navigation scenario using range and elevation measurements. The estimation accuracies and the processing times for different algorithms are compared for the scenario. The result demonstrates that the UKF provides better accuracy than the EKF but requires more processing time. The SPUKF accuracy is better than the EKF and the processing time is significantly less than the UKF. However, the accuracy of the SPUKF is less than the UKF. The ESPUKF provides estimation accuracy comparable to the UKF and the processing time is also significantly reduced.

eess.SY↗

arXiv2016

A Novel a priori State Computation Strategy for the Unscented Kalman Filter to Improve Computational Efficiency

A priori state vector and error covariance computation for the Unscented Kalman Filter (UKF) is described. The original UKF propagates multiple sigma points to compute the a priori mean state vector and the error covariance, resulting in a higher computational time compared to the Extended Kalman Filter (EKF). In the proposed method, the posterior mean state vector is propagated and then the sigma points at the current time step are calculated using the first-order Taylor Series approximation. This reduces the computation time significantly, as demonstrated using two example applications which show improvements of 90.5% and 92.6%. This method shows the estimated state vector and the error covariance are accurate to the first-order Taylor series terms. A second method using Richardson Extrapolation improves prediction accuracy to the second-order Taylor series terms. This is implemented on the two examples, improving efficiency by 85.5% and 86.8%.

math.OC↗

arXiv2016

Representations of Rota-Baxter algebras and regular singular decompositions

There is a Rota-Baxter algebra structure on the field $A=\mathbf{k}((t))$ with $ P$ being the projection map $A=\mathbf{k}[[t]]\oplus t^{-1}\mathbf{k}[t^{-1}]$ onto $ \mathbf{k}[[ t]]$. We study the representation theory and regular-singular decompositions of any finite dimensional $A$-vector space. The main result shows that the category of finite dimensional representations is semisimple and consists of exactly three isomorphism classes of irreducible representations which are all one-dimensional. As a consequence, the number of $GL_A(V)$-orbits in the set of all regular-singular decompositions of an $n$-dimensional $ A$-vector space $V$ is $(n+2)(n+1)/2$. We also use the result to compute the generalized class number, i.e., the number of the $GL_n(A)$-isomorphism classes of finitely generated $\mathbf{k}[[t]]$-submodules of $A^n$.

math.RT↗