The Extended Preferred Ordering Theorem for Radar Tracking Using the Extended Kalman Filter

A certain problem in nonlinear estimation exists in radar tracking. Usually radar detections provide instantaneous position measurements in radar (polar) coordinates at discrete times, while tracks (estimated positions and motions over continuous time) are determined in rectangular coordinates; and the linear Kalman filter (LKF) is used as the estimator. Less common, the LKF is used to determine the tracks in radar coordinates, which are then converted into rectangular coordinates. Rarely is the extended Kalman filter (EKF) used, where the tracks are directly determined in rectangular coordinates from the radar detections via a local linearization. And so most radar tracks tend to be biased - and their Kalman covariance matrices are inconsistent with the true ones. Of course, some techniques have been proposed for debiasing them and making their mean squared errors consistent with the covariance matrices determined by the tracking filter. It is shown here, however, that the leading one for debiasing the LKF can make the biases worse; and a remedy for that is provided. But the focus is upon the EKF. In an earlier work by this author - dubbed the Preferred Ordering Theorem (POT) - it was shown that the linearization errors in range of the EKF can be virtually eliminated by using the measurement components of a detection recursively in a certain order: azimuth first and range last. But that has a fundamental limitation, namely, that preferred order. And so here a new version is provided, dubbed the Extended-POT (EPOT). Not only can the EPOT be more efficient than the POT in certain settings, but under it the measurements may be used in any order with virtually the same results

Bis[μ-pentane-2,4-dionato(1−)]bis­{aqua­[1,1,1,5,5,5-hexa­fluoro­pentane-2,4-dionato(1−)]cobalt(II)}

The title complex, [Co2(C5HF6O2)2(C5H7O2)2(H2O)2], is centrosymmetric with a crystallographic inversion center in the middle of the mol­ecule. The octa­hedrally coordinated CoII atoms are bridged by two chelating acetyl­acetonate (acac) ligands and two more electron-poor 1,1,1,5,5,5-hexa­fluoro­pentane-2,4-dionato (hfac) ligands are bonded terminally in a solely chelating manner. The coordinated water mol­ecules form inter­molecular O—H⋯O hydrogen bonds with electron-rich acac O atoms of neighboring mol­ecules, leading to strings of mol­ecules along the a axis

The Distributed Array Descriptor for a PCRC HPF Compiler Version 2.0 SCCS-770d

We describe a distributed array descriptor that can be used by a runtime supporting HPFlike compilers. This descriptor captures all five types of alignment and BLOCK and CYCLIC distribution as defined in HPF specification. In essence, this descriptor does not distinguish whole array and array sections. Prior to this version, we had versions 1.0, 1.1, and 1.2. This version is not only an update of previous versions, but more importantly it also directly reflects our current practice in an HPF compilation effort

Reactivity and electronic structure of aluminum clusters: The aluminum-nitrogen system

The stability of anionic aluminum–nitrogen clusters has been examined and Al2N−, Al3N−2,Al5N−2, Al6N−3, Al8N−3, and Al9N−2 are found to be particularly stable. Theoreticaldensity functional calculations on neutral and anionic AlnN (n=1–8) clusters were performed and the stability and reaction energetics with oxygen examined. Clusters requiring less than 5.7 eV to remove an electron and an Al atom are shown to be resistant to the reaction with oxygen

trans-Dimethano­lbis(1,1,1-trifluoro-5,5-dimethyl­hexane-2,4-dionato)zinc(II)

The title compound, [Zn(C8H10F3O2)2(CH4O)2], is a dimethanol coordinated zinc complex with the acetyl acetonate derivative 1,1,1-trifluoro-5,5-dimethyl­hexane-2,4-dionate. The bis­-β-diketonate complex, which is isostructural with its Co analogue, is located on a crystallographic inversion center. The complex is octa­hedral with basically no distortion, and the methanol mol­ecules are in trans positions with respect to one another. The planes of the β-diketonate and the ZnO4 unit are tilted by 18.64 (10)° against each other. O—H⋯O hydrogen bonds between the methanol hydroxyl groups and neighboring diketonate O atoms create chains running along [100]

cis-[Aqua/methanol(0.45/1.55)](1,1,1-trifluoro-5,5-dimethyl­hexane-2,4-dionato)nickel(II)–cis-[aqua/methanol(1.49/0.51)](1,1,1-trifluoro-5,5-dimethyl­hexane-2,4-dionato)nickel(II) (1/1)

The title compound, [Ni(C8H10F3O2)2(CH4O)1.55(H2O)0.45][Ni(C8H10F3O2)2(CH4O)0.51(H2O)1.49], is an octa­hedral nickel(II) complex with two acetyl­acetonate-like 1,1,1-trifluoro-5,5-dimethyl­hexane-2,4-dionate ligands. The two chelating ligands are in cis positions with respect to each other and the remaining two adjacent coordination sites are taken up by water and methanol donor mol­ecules. In both crystallographically independent mol­ecules, each donor site shows disorder of methanol and water with occupancies of 0.51 (1) and 0.55 (1) in favor of methanol. The remaining two donor sites are not disordered and are water for the first and methanol for the second independent mol­ecule. Rotational disorder is observed for one of the tert-butyl groups, the occupancy rate for the major component here is 0.687 (9). O—H⋯O hydrogen bonds connect the two independent mol­ecules with each other and, across a crystallographic inversion center, they are combined with two neighboring mol­ecules to form a centrosymmetric hydrogen-bonded tetra­mer

Mass spectrometric and first principles study of Aln_nC−^- clusters

We study the carbon-dope aluminum clusters by using time-of-flight mass spectrum experiments and {\em ab initio} calculations. Mass abundance distributions are obtained for anionic aluminum and aluminum-carbon mixed clusters. Besides the well-known magic aluminum clusters such as Al$_{13}^-$ and Al$_{23}^-$, Al$_7$C$^-$ cluster is found to be particularly stable among those Al$_n$C$^-$ clusters. Density functional calculations are performed to determine the ground state structures of Al$_n$C$^-$ clusters. Our results show that the Al$_7$C$^-$ is a magic cluster with extremely high stability, which might serve as building block of the cluster-assembled materials.Comment: 4 pages, 6 figure