This article deals with the recursive filtering problem for nonlinear time-varying stochastic systems subject to possible measurement outliers. In order mitigate effects from abnormal measurements, we construct a filter saturation constraint imposed on innovations where level is adaptively determined according estimation errors. Two performance indices, namely, finite-horizon H <sub xmlns:mml="...

LEO satellite mega-constellation projects have been proposed by many countries or commercial organizations in recent years. With more than 2000 satellites launched SpaceX to configure the Starlink system, orbital resources are constrained given existence of spacecrafts and countless debris. Due this, operating environment is full uncertainty information symmetry absent for designers stakeholder...

In these notes we first offer an overview of two core areas in the dynamics of probability measure preserving systems, the Kolmogorov-Sinai theory of entropy and the theory of orbit equivalence. Entropy is a nontrivial invariant that, said simply, measures the exponential growth rate of the number of orbits in a dynamical system, a very rough measure of the complexity of the orbit structure. On...

We recall that a probability measure ν on X is said to be μ-stationary if one has μ ∗ ν = ν. It is then said to be μ-ergodic if it is extremal among μ-stationary probability measures. We will say that a probability measure ν on X is homogeneous if it is supported by a closed orbit F of its stabilizer Gν := {g ∈ G | g∗ν = ν}. Such a probability is a finite average of probability measures which a...

Orbit determination in application to the estimation of impact probability has the goal of determining the evolution of the state probability density function (pdf) and determining a measure of the probability of collision. Nonlinear gravitational interaction and non-conservative forces can make the pdf far from Gaussian. This work implements three nonlinear sequential estimators: the Extended ...

This paper describes a discrete-time retrial queue and shows how importance sampling simulations can be applied for estimating the probability of large orbit content and the overflow fraction of primary calls.