— Holonomic and semi-holonomic geometries modelled on a homogeneous space G/P are introduced as reductions of the holonomic or semi-holonomic frame bundles respectively satisfying a straightforward generalization of the partial differential equation characterizing torsion–free linear connections. Under a suitable regularity assumption on the model space G/P we establish an equivalence of catego...

This paper addresses a new design method of recursive least-squares (RLS) and finite impulse response (FIR) filter, using covariance information, in linear continuous-time stochastic systems. The signal process is observed with additive white noise. It is assumed that the white observation noise is independent of the signal process. The auto-covariance function of the signal is expressed in the...

A nonlinear semi-analytic filtering method to sequentially estimate spacecraft states and their associated uncertainties is presented. We first discuss the state transition tensors that characterize the localized nonlinear behavior of the spacecraft trajectory and illustrate the importance of higher order effects on orbit uncertainty propagation. We then present the semi-analytic filtering meth...

Let $G$ be a group and $H$ a subgroup of $G$‎. ‎ $H$ is said to have semi-$Pi$-property in $G$ if there is a subgroup $T$ of $G$ such that $G=HT$ and $Hcap T$ has $Pi$-property in $T$‎. ‎In this paper‎, ‎investigating on semi-$Pi$-property of subgroups‎, ‎we shall obtain some new description of finite groups‎.

In this study, we investigate the further properties of quasi irresolute topological groups defined in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connected quasi irresolute topological group $(G,*,tau )$, if $V$ is any symmetric semi-open neighborhood of $e_G$, then...

This letter proposes to apply the Kalman-like observer paradigm general nonlinear systems by linearization along estimated trajectory, similarly an Extended Kalman Filter. The main difference is that quadratic Riccati equation replaced a linear Lyapunov which can be solved and explicitly related determinability Gramian. allows show analysis without any ad-hoc assumption on solution, resulting o...

For nonstationary time series consisting ofmultiple time-varying frequency (TVF) componentswhere the frequency of components overlaps in time, classical linear filters fail to extract components. The G-filter based on time deformation has been developed to extract components of multicomponent G-stationary processes. In this paper, we explore the wide application of the G-filter for filtering di...