Finite-dimensional filters with nonlinear drift. V: solution to Kolmogorov equation arising from linear filtering with non-Gaussian initial condition

Despite its usefulness, the Kalman-Bucy filter is not perfect. One of its weaknesses is that it needs a Gaussian assumption on the initial data. Recently Yau and Yau introduced a new direct method to solve the estimation problem for linear filtering with non-Gaussian initial data. They factored the problem into two parts: (1) the on-line solution of a finite system of ordinary differential equations (ODEs), and (2) the off-line calculation of the Kolmogorov equation. Here we derive an explicit closed-form solution of the Kolmogorov equation. We also give some properties and conduct a numerical study of the solution.     

Interference between FM Carriers and a Digitally Modulated SCPC Circuit

The interference from the digital single channel per carrier (SCPC) circuits into frequency-modulated carrier systems has been calculated by convolving the desired and the interfering spectra extending the previously published works. Resulting interference noise power in FDM/FM systems covering a wide range of modulation indices and basebands has been presnted. Also plots of interference noise power as a function of the number of SCPC circuits have been presented for various values of carrier power to interference power ratios.     

Novel wideband multimode hybrid interferometer system

In this paper, a novel hybrid of a three-element interferometer comprised of multimode antennas is analyzed. The phase ambiguities associated with the long baselines of the interferometer are resolved using the "coarse" angle estimates provided by the multimode antenna. This results in the elimination of the short baseline interferometers of the conventional five-element interferometer. It is shown here that the signal-to-noise ratio (SNR) must be above a threshold value to resolve the phase ambiguities with a high degree of probability. An expression that shows the dependence of this threshold SNR on the interferometer spacing and the variance of the angle estimates provided by the multimode antenna is derived. A single three-element wideband multimode antenna interferometer can replace several five-element conventional interferometers, each covering a separate frequency band.     

Matched Filter Criteria and Range Weighting for Weather Radar

The effective weighting function for weather radar is defined. This weighting function considers the effects of both the transmitted signal and the receiver filter. It is used to assign effective ranges to samples taken at prescribed times. For uniformly distributed targets it is shown that "signal"-to-noise ratio depends on the receiver filter, transmitted signal envelope, and receiver noise spectral density. Maximization of this signal-to-noise ratio when range resolution constraints are imposed is discussed, and a receiver design approach specifically adapted for Doppler weather radars is developed.     

Calibration of the MERIC full-polarimetric radar: theory and implementation

This paper describes the architecture and calibration design of the experimental ground based radar station MERIC. This full-polarimetric radar is conceived for the analysis and the recognition of non cooperative aircraft in flight.We carefully study how the full-polarimetric capability is obtained for a simultaneous transmit (simultaneous transmission of two linear FM with opposite slopes) radar system, using analogue deramping with a replica.The phase distortions of the signal propagating in the four polarimetric channels are carefully estimated. We define a phase calibrating method compatible with the outdoor measurements conditions and few constraints on reference targets.We show the phase accuracy obtained with the proposed calibration method on real measurements.     

An Optimum Phase Reference Detector for Fully Modulated Phase-Shift Keyed Signals

Many modern telemetry systems which use phase-shift keying (PSK) have receivers which derive a coherent reference from the fully modulated PSK signal itself and thus conserve the energy which otherwise would be allocated to a discrete reference signal. In this paper, an optimum receiver structure for estimating a phase reference from the PSK signal itself is derived and its realization discussed. It is shown that at low signal-to-noise ratios, the optimum detector can be realized with a Costas loop. Since a Costas loop and squaring loop exhibit identical performance, it follows that either of these simple devices gives optimum performance for low-input signal-to-noise ratios.     

Magnetosphere Imaging Instrument (MIMI) on the Cassini Mission to Saturn/Titan

The magnetospheric imaging instrument (MIMI) is a neutral and charged particle detection system on the Cassini orbiter spacecraft designed to perform both global imaging and in-situ measurements to study the overall configuration and dynamics of Saturn’s magnetosphere and its interactions with the solar wind, Saturn’s atmosphere, Titan, and the icy satellites. The processes responsible for Saturn’s aurora will be investigated; a search will be performed for substorms at Saturn; and the origins of magnetospheric hot plasmas will be determined. Further, the Jovian magnetosphere and Io torus will be imaged during Jupiter flyby. The investigative approach is twofold. (1) Perform remote sensing of the magnetospheric energetic (E > 7 keV) ion plasmas by detecting and imaging charge-exchange neutrals, created when magnetospheric ions capture electrons from ambient neutral gas. Such escaping neutrals were detected by the Voyager l spacecraft outside Saturn’s magnetosphere and can be used like photons to form images of the emitting regions, as has been demonstrated at Earth. (2) Determine through in-situ measurements the 3-D particle distribution functions including ion composition and charge states (E > 3 keV/e). The combination of in-situ measurements with global images, together with analysis and interpretation techniques that include direct “forward modeling’’ and deconvolution by tomography, is expected to yield a global assessment of magnetospheric structure and dynamics, including (a) magnetospheric ring currents and hot plasma populations, (b) magnetic field distortions, (c) electric field configuration, (d) particle injection boundaries associated with magnetic storms and substorms, and (e) the connection of the magnetosphere to ionospheric altitudes. Titan and its torus will stand out in energetic neutral images throughout the Cassini orbit, and thus serve as a continuous remote probe of ion flux variations near 20R _S (e.g., magnetopause crossings and substorm plasma injections). The Titan exosphere and its cometary interaction with magnetospheric plasmas will be imaged in detail on each flyby. The three principal sensors of MIMI consists of an ion and neutral camera (INCA), a charge–energy–mass-spectrometer (CHEMS) essentially identical to our instrument flown on the ISTP/Geotail spacecraft, and the low energy magnetospheric measurements system (LEMMS), an advanced design of one of our sensors flown on the Galileo spacecraft. The INCA head is a large geometry factor (G ∼ 2.4 cm² sr) foil time-of-flight (TOF) camera that separately registers the incident direction of either energetic neutral atoms (ENA) or ion species (≥5^∘ full width half maximum) over the range 7 keV/nuc < E < 3 MeV/nuc. CHEMS uses electrostatic deflection, TOF, and energy measurement to determine ion energy, charge state, mass, and 3-D anisotropy in the range 3 ≤ E ≤ 220 keV/e with good (∼0.05 cm² sr) sensitivity. LEMMS is a two-ended telescope that measures ions in the range 0.03 ≤ E ≤ 18 MeV and electrons 0.015 ≤ E≤ 0.884 MeV in the forward direction (G ∼ 0.02 cm² sr), while high energy electrons (0.1–5 MeV) and ions (1.6–160 MeV) are measured from the back direction (G ∼ 0.4 cm² sr). The latter are relevant to inner magnetosphere studies of diffusion processes and satellite microsignatures as well as cosmic ray albedo neutron decay (CRAND). Our analyses of Voyager energetic neutral particle and Lyman-α measurements show that INCA will provide statistically significant global magnetospheric images from a distance of ∼60 R _S every 2–3 h (every ∼10 min from ∼20 R _S). Moreover, during Titan flybys, INCA will provide images of the interaction of the Titan exosphere with the Saturn magnetosphere every 1.5 min. Time resolution for charged particle measurements can be < 0.1 s, which is more than adequate for microsignature studies. Data obtained during Venus-2 flyby and Earth swingby in June and August 1999, respectively, and Jupiter flyby in December 2000 to January 2001 show that the instrument is performing well, has made important and heretofore unobtainable measurements in interplanetary space at Jupiter, and will likely obtain high-quality data throughout each orbit of the Cassini mission at Saturn. Sample data from each of the three sensors during the August 18 Earth swingby are shown, including the first ENA image of part of the ring current obtained by an instrument specifically designed for this purpose. Similarily, measurements in cis-Jovian space include the first detailed charge state determination of Iogenic ions and several ENA images of that planet’s magnetosphere.This revised version was published online in July 2005 with a corrected cover date.     

A Possible Transfer Mechanism for the 11-Year Solar Cycle to the Lower Stratosphere

Observational evidence of the 11-year solar cycle (SC) modulation of stratosphere temperatures and winds from the ERA-40 dataset is reviewed, with emphasis on the Northern winter hemisphere. A frequency modulation of sudden warming events is noted, with warmings occurring earlier in solar minimum periods than in solar maximum periods. The observed interaction between the influence of the SC and the quasi biennial oscillation (QBO) on the frequency of sudden warmings is noted as a possible clue for understanding their mechanism of influence. A possible transfer route for the 11-year solar cycle from the equatorial stratopause region to the lowest part of the stratosphere is proposed, via an influence on sudden warming events and the associated induced meridional circulation. SC and QBO composites of zonal wind anomalies show anomalous wind distributions in the subtropical upper stratosphere in early winter. Mechanistic model experiments are reviewed that demonstrate a sensitivity of sudden warmings to small wind anomalies in this region. Various diagnostics from these experiments are shown, including EP fluxes and their divergence and also the synoptic evolution of the polar vortex, in order to understand the mechanism of the influence. Some recent GCM experiments to investigate the SC/QBO interaction are also described. They simulate reasonably well the observed SC/QBO interaction of sudden warming events and appear to support the hypothesis that tropical/subtropical upper stratospheric wind anomalies are an important influence on the timing of sudden warmings.     

Deep Impact: Working Properties for the Target Nucleus – Comet 9P/Tempel 1

In 1998, Comet 9P/Tempel 1 was chosen as the target of the Deep Impact mission (A’Hearn, M. F., Belton, M. J. S., and Delamere, A., Space Sci. Rev., 2005) even though very little was known about its physical properties. Efforts were immediately begun to improve this situation by the Deep Impact Science Team leading to the founding of a worldwide observing campaign (Meech et al., Space Sci. Rev., 2005a). This campaign has already produced a great deal of information on the global properties of the comet’s nucleus (summarized in Table I) that is vital to the planning and the assessment of the chances of success at the impact and encounter. Since the mission was begun the successful encounters of the Deep Space 1 spacecraft at Comet 19P/Borrelly and the Stardust spacecraft at Comet 81P/Wild 2 have occurred yielding new information on the state of the nuclei of these two comets. This information, together with earlier results on the nucleus of comet 1P/Halley from the European Space Agency’s Giotto, the Soviet Vega mission, and various ground-based observational and theoretical studies, is used as a basis for conjectures on the morphological, geological, mechanical, and compositional properties of the surface and subsurface that Deep Impact may find at 9P/Tempel 1. We adopt the following working values (circa December 2004) for the nucleus parameters of prime importance to Deep Impact as follows: mean effective radius = 3.25± 0.2 km, shape – irregular triaxial ellipsoid with a/b = 3.2± 0.4 and overall dimensions of ∼14.4 × 4.4 × 4.4 km, principal axis rotation with period = 41.85± 0.1 hr, pole directions (RA, Dec, J2000) = 46± 10, 73± 10 deg (Pole 1) or 287± 14, 16.5± 10 deg (Pole 2) (the two poles are photometrically, but not geometrically, equivalent), Kron-Cousins (V-R) color = 0.56± 0.02, V-band geometric albedo = 0.04± 0.01, R-band geometric albedo = 0.05± 0.01, R-band H(1,1,0) = 14.441± 0.067, and mass ∼7×10¹³ kg assuming a bulk density of 500 kg m⁻³. As these are working values, {i.e.}, based on preliminary analyses, it is expected that adjustments to their values may be made before encounter as improved estimates become available through further analysis of the large database being made available by the Deep Impact observing campaign. Given the parameters listed above the impact will occur in an environment where the local gravity is estimated at 0.027–0.04 cm s⁻² and the escape velocity between 1.4 and 2 m s⁻¹. For both of the rotation poles found here, the Deep Impact spacecraft on approach to encounter will find the rotation axis close to the plane of the sky (aspect angles 82.2 and 69.7 deg. for pole 1 and 2, respectively). However, until the rotation period estimate is substantially improved, it will remain uncertain whether the impactor will collide with the broadside or the ends of the nucleus.     

Comparison of ≳40 keV Electron Events at High and Low Heliolatitudes: Ulysses/HI-SCALE and ACE/EPAM

We have performed a joint survey of anisotropic ≳40 keV electron events from August 1997 to September 2000 using the matched detectors on the Ulysses (ULS)/HI-SCALE and the ACE/EPAM instruments. A computer algorithm selected events with strong, statistically significant pitch-angle anisotropies. Electron pitch-angle distributions at ACE (∼1 AU) are often ‘beams’ that are strongly collimated along the local interplanetary magnetic field (IMF). These flare-associated impulsive injections can display rapid rise times (∼15 min) and slower decays, or more irregular intensity histories. At ULS, the electron intensities are lower and the time histories smoother, but strong anisotropies are still observable, indicating direct, nearly field-aligned propagation outward from the Sun. We focus on four event periods, selected from the survey, during times when the angle between the footpoints of the IMF lines intersecting ACE and ULS is small. These events span three full years and cover a wide range of distances and heliographic latitudes. We found one reasonably good association between impulsive electron events at ACE and ULS, and two events with small field-aligned gradients. This revised version was published online in August 2006 with corrections to the Cover Date.