An analysis of GDOP in global positioning system navigation

The accuracy of user navigation fix based on the NAVSTAR global positioning system is described. The trace of this matrix serves as a convenient navigation performance index and the square root of the trace is called geometric dilution of precision (GDOP). Certain theoretical results concerning the general properties of the navigation performance are derived. An efficient algorithm for the computation of GDOP is given. Applications of the results are illustrated by numerical examples

A general geometric theory of attitude determination from directional sensing

A general geometric theory of spacecraft attitude determination from external reference direction sensors was presented. Outputs of different sensors are reduced to two kinds of basic directional measurements. Errors in these measurement equations are studied in detail. The partial derivatives of measurements with respect to the spacecraft orbit, the spacecraft attitude, and the error parameters form the basis for all orbit and attitude determination schemes and error analysis programs and are presented in a series of tables. The question of attitude observability is studied with the introduction of a graphical construction which provides a great deal of physical insight. The result is applied to the attitude observability of the IMP-8 spacecraft

Tri-Dirac Surface Modes in Topological Superconductors

We propose a new type of topological surface modes having cubic dispersion in three-dimensional topological superconductors. Lower order dispersions are prohibited by the threefold rotational symmetry and time-reversal symmetry. Cooper pairing in the bulk changes sign under improper rotations, akin to$^{3}$He-B. The surface manifestations are a divergent surface density of states at the Fermi level and isospins that rotate three times as they circle the origin in momentum space. We propose that Heusler alloys with band inversion are candidate materials to harbor the novel topological superconductivity.Comment: Five-page main text plus five-page supplementary materials; three figure

Entanglement Spectrum Classification of CnC_n-invariant Noninteracting Topological Insulators in Two Dimensions

We study the single particle entanglement spectrum in 2D topological insulators which possess $n$-fold rotation symmetry. By defining a series of special choices of subsystems on which the entanglement is calculated, or real space cuts, we find that the number of protected in-gap states for each type of these real space cuts is a quantum number indexing (if any) non-trivial topology in these insulators. We explicitly show the number of protected in-gap states is determined by a $Z^n$-index, $(z_1,...,z_n)$, where $z_m$ is the number of occupied states that transform according to $m$-th one-dimensional representation of the $C_n$ point group. We find that the entanglement spectrum contains in-gap states pinned in an interval of entanglement eigenvalues $[1/n,1-1/n]$. We determine the number of such in-gap states for an exhaustive variety of cuts, in terms of the $Z_m$ quantum numbers. Furthermore, we show that in a homogeneous system, the $Z^n$ index can be determined through an evaluation of the eigenvalues of point group symmetry operators at all high-symmetry points in the Brillouin zone. When disordered $n$-fold rotationally symmetric systems are considered, we find that the number of protected in-gap states is identical to that in the clean limit as long as the disorder preserves the underlying point group symmetry and does not close the bulk insulating gap.Comment: 14.2 pages for main text, 4.8 pages for Appendices, four figures and two table

Constraints on primordial black holes and primeval density perturbations from the epoch of reionization

We investigate the constraint on the abundance of primordial black holes (PBHs) and the spectral index $n$ of primeval density perturbations given by the ionizing photon background at the epoch of reionization. Within the standard inflationary cosmogony, we show that the spectral index $n$ of the power-law power spectrum of primeval density perturbations should be $n<$1.27. Since the universe is still optical thick at the reionization redshift $z\sim 6$ - 8, this constraint is independent of the unknown parameter of reheating temperature of the inflation. The ionizing photon background from the PBHs can be well approximated by a power law spectrum $J(\nu)\propto{\nu}^3$, which is greatly different from those given by models of massive stars and quasars.Comment: 4 pages, 3 eps figues, to be published in ApJ Letter

Large Chern Number Quantum Anomalous Hall Effect In Thin-film Topological Crystalline Insulators

Quantum anomalous Hall (QAH) insulators are two-dimensional (2D) insulating states exhibiting properties similar to those of quantum Hall states but without external magnetic field. They have quantized Hall conductance $\sigma^H=Ce^2/h$, where integer $C$ is called the Chern number, and represents the number of gapless edge modes. Recent experiments demonstrated that chromium doped thin-film (Bi,Sb)$_2$Te$_3$ is a QAH insulator with Chern number $C=\pm1$. Here we theoretically predict that thin-film topological crystalline insulators (TCI) can host various QAH phases, when doped by ferromagnetically ordered dopants. Any Chern number between $\pm4$ can, in principle, be reached as a result of the interplay between (a) the induced Zeeman field, depending on the magnetic doping concentration, (b) the structural distortion, either intrinsic or induced by a piezoelectric material through proximity effect and (c) the thickness of the thin film. The tunable Chern numbers found in TCI possess significant potential for ultra-low power information processing applications.Comment: References update

New class of topological superconductors protected by magnetic group symmetries

We study a new type of three-dimensional topological superconductors that exhibit Majorana zero modes (MZM) protected by a magnetic group symmetry, a combined antiunitary symmetry composed of a mirror reflection and time-reversal. This new symmetry enhances the noninteracting topological classification of a superconducting vortex from $Z_2$ to $Z$, indicating that multiple MZMs can coexist at the end of one magnetic vortex of unit flux. Specially, we show that a vortex binding two MZMs can be realized on the $(001)$-surface of a topological crystalline insulator SnTe with proximity induced BCS Cooper pairing, or in bulk superconductor In$_x$Sn$_{1-x}$Te.Comment: Accepted version to appear in PRL: 4-page text plus 4-page supplementary materials, two figure

ALTKAL: An optimum linear filter for GEOS-3 altimeter data

ALTKAL is a computer program designed to smooth sea surface height data obtained from the GEOS 3 altimeter, and to produce minimum variance estimates of sea surface height and sea surface slopes, along with their standard derivations. The program operates by processing the data through a Kalman filter in both the forward and backward directions, and optimally combining the results. The sea surface height signal is considered to have a geoid signal, modeled by a third order Gauss-Markov process, corrupted by additive white noise. The governing parameters for the signal and noise processes are the signal correlation length and the signal-to-noise ratio. Mathematical derivations of the filtering and smoothing algorithms are presented. The smoother characteristics are illustrated by giving the frequency response, the data weighting sequence and the transfer function of a realistic steady-state smoother example. Based on nominal estimates for geoidal undulation amplitude and correlation length, standard deviations for the estimated sea surface height and slope are 12 cm and 3 arc seconds, respectively