Differential-game-based guidance law using target orientation observations

Modern 4th generation air-to-air missiles are quite capable of dealing with today's battlefield needs. Advanced aerodynamics, highly efficient warheads and smart target acquisition systems combine to yield higher missile lethality than ever. However, in order to intercept highly maneuverable targets, such as future unmanned combat air vehicles (UCAV), or to achieve higher tracking precision for missiles equipped with smaller warheads, further improvement in the missile guidance system is still needed. A new concept is presented here for deriving improved differential-game-based guidance laws that make use of information about the target orientation, which is acquired via an imaging seeker. The underlying idea is that of using measurements of the target attitude as a leading indicator of target acceleration. Knowledge of target attitude reduces the reachable set of target acceleration, facilitating the computation of an improved estimate of the zero-effort miss (ZEM) distance. In consequence, missile guidance accuracy is significantly improved. The new concept is applied in a horizontal interception scenario, where it is assumed that the target maneuver direction, constituting a partial attitude information, can be extracted via processing target images, acquired by an imaging sensor. The derivation results in a new guidance law that explicitly exploits the direction of the target acceleration. The performance of the new guidance law is studied via a computer simulation, which demonstrates its superiority over existing state-of-the-art differential-game-based guidance laws. It is demonstrated that a significant decrease in the miss distance can be expected via the use of partial target orientation information.     

Expectations for Infrared Spectroscopy of 9P/Tempel 1 from Deep Impact

The science payload on the Deep Impact mission includes a 1.05–4.8 μm infrared spectrometer with a spectral resolution ranging from R∼200–900. The Deep Impact IR spectrometer was designed to optimize, within engineering and cost constraints, observations of the dust, gas, and nucleus of 9P/Tempel 1. The wavelength range includes absorption and emission features from ices, silicates, organics, and many gases that are known to be, or anticipated to be, present on comets. The expected data will provide measurements at previously unseen spatial resolution before, during, and after our cratering experiment at the comet 9P/Tempel 1. This article explores the unique aspects of the Deep Impact IR spectrometer experiment, presents a range of expectations for spectral data of 9P/Tempel 1, and summarizes the specific science objectives at each phase of the mission.     

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.     

Detection of chi-square fluctuating targets in arbitrary clutter

In a recent paper, general expressions were derived for the density and cumulative probability functions of the amplitude of a linear matched-filter output given a nonfluctuating target in a clutter-limited environment. These expressions were based on the clutter amplitude density function. The results are extended to calculate the cumulative probability function of the output of a linear matched filter used to detect a chi-square fluctuating target in a clutter-limited environment. The resulting method is applied to a common radar clutter model, and experimental sonar data.     

Refractive Errors in Angle-of-Elevation Measurements

It is shown that the errors associated with radio elevation measurements may be investigated systematically using a variational technique. The error occurring when spaced antennas are used is compared with that for a single directional antenna. Integral expressions are obtained for the refractive errors.     

On Optimal Allocation and Guidance Laws for Linear lnterception and Rendezvous Problems

This paper considers the problem of guiding N interceptors so that they intercept or rendezvous with N targets at the same time T. It is assumed that the interceptors and targets are described by linear time-varying differential equations (deterministic or stochastic). Under certain assumptions both the optimal (static or dynamic) interceptor-target allocation and the guidance of each interceptor for the optimal allocation can be obtained with modest real-time and storage computer requirements.     

Tracking Performance of a Monopulse Radar in the Presence of Multiple Targets

The equations derived by A. J. Rainal for the probability density function of the angle error output of a monopulse radar excited by a Gaussian signal and Gaussian thermal noise are generalized to include the presence of multiple targets. The examples given demonstrate the radar's behavior for various combinations of target and noise parameters.     

Present-Day Sea Level Change: Observations and Causes

We investigate climate-related processes causing variations of the global mean sea level on interannual to decadal time scale. We focus on thermal expansion of the oceans and continental water mass balance. We show that during the 1990s where global mean sea level change has been measured by Topex/Poseidon satellite altimetry, thermal expansion is the dominant contribution to the observed 2.5 mm/yr sea level rise. For the past decades, exchange of water between continental reservoirs and oceans had a small, but not totally negligible contribution (about 0.2 mm/yr) to sea level rise. For the last four decades, thermal contribution is estimated to about 0.5 mm/yr, with a possible accelerated rate of thermosteric rise during the 1990s. Topex/Poseidon shows an increase in mean sea level of 2.5 mm/yr over the last decade, a value about two times larger than reported by historical tide gauges. This would suggest that there has been significant acceleration of sea level rise in the recent past, possibly related to ocean warming. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Genesis Solar-Wind Collector Materials

Genesis (NASA Discovery Mission #5) is a sample return mission. Collectors comprised of ultra-high purity materials will be exposed to the solar wind and then returned to Earth for laboratory analysis. There is a suite of fifteen types of ultra-pure materials distributed among several locations. Most of the materials are mounted on deployable panels (‘collector arrays’), with some as targets in the focal spot of an electrostatic mirror (the ‘concentrator’). Other materials are strategically placed on the spacecraft as additional targets of opportunity to maximize the area for solar-wind collection. Most of the collection area consists of hexagonal collectors in the arrays; approximately half are silicon, the rest are for solar-wind components not retained and/or not easily measured in silicon. There are a variety of materials both in collector arrays and elsewhere targeted for the analyses of specific solar-wind components. Engineering and science factors drove the selection process. Engineering required testing of physical properties such as the ability to withstand shaking on launch and thermal cycling during deployment. Science constraints included bulk purity, surface and interface cleanliness, retentiveness with respect to individual solar-wind components, and availability. A detailed report of material parameters planned as a resource for choosing materials for study will be published on a Genesis website, and will be updated as additional information is obtained. Some material is already linked to the Genesis plasma data website (genesis.lanl.gov). Genesis should provide a reservoir of materials for allocation to the scientific community throughout the 21st Century. This revised version was published online in August 2006 with corrections to the Cover Date.     

Variations of the magnetic fields in large solar flares

We present preliminary results from high resolution observations obtained with the Michelson Doppler Imager (MDI) instrument on the SOHO of two large solar flares of 14 July 2000 and 24 November 2000. We show that rapid variations of the line-of-sight magnetic field occured on a time scale of a few minutes during the flare explosions. The reversibility/irreversibility of the magnetic field of both active regions is a very good tool for understanding how the magnetic energy is released in these flares. The observed sharp increase of the magnetic energy density at the time of maximum of the solar flare could involve an unknown component which deposited supplementary energy into the system. This revised version was published online in August 2006 with corrections to the Cover Date.