Planning of refracted starlight observation based on observability analysis

In traditional observation schemes of stellar refraction navigation, the accuracy was limited due to unreasonable observation directions. In order to ameliorate this situation, a method of refracted starlight observation based on observability analysis is proposed. The function of this method is optimally generating an observation attitude sequence according to standard trajectories of spacecraft so that the selection of a refracted starlight observation sequence can be realized. Specifically, the improvement of Fisher information matrix calculation enables this method to be qualified for the navigation problem with unsteady measurement quantities as well as the non-fully observability which is defined as the capability of estimating the system state through measurements in finite time. Here, we construct a quantitative relationship between refracted starlight measurements and system observability by means of Fisher information index ( FII). Next, the observation scheme is retrieved by searching the maximum value of the optimized variable, which includes the ( FII). Finally, we resort to the extended Kalman filter to accomplish typical trajectory navigation simulations of the observation scheme. The results indicate that our method brings more accuracy than traditional ones in estimation of position and velocity of the optimal observation scheme.

The Maximal Strichartz Family of Gaussian Distributions: Fisher Information, Index of Dispersion, and Stochastic Ordering

We define and study several properties of what we callMaximal Strichartz Family of Gaussian Distributions. This is a subfamily of the family of Gaussian Distributions that arises naturally in the context of theLinear Schrödinger Equationand Harmonic Analysis, as the set of maximizers of certain norms introduced by Strichartz. From a statistical perspective, this family carries with itself some extrastructure with respect to the general family of Gaussian Distributions. In this paper, we analyse this extrastructure in several ways. We first compute theFisher Information Matrixof the family, then introduce some measures ofstatistical dispersion, and, finally, introduce aPartial Stochastic Orderon the family. Moreover, we indicate how these tools can be used to distinguish between distributions which belong to the family and distributions which do not. We show also that all our results are in accordance with the dispersive PDE nature of the family.