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.     

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.     

Detecting moving targets in SAR imagery by focusing

A new method for detecting moving targets in a synthetic aperture radar (SAR) image is presented. It involves segmenting a complex-valued SAR image into patches, focusing each patch separately, and measuring the sharpness increase in the focused patch. The algorithm is sensitive to azimuth velocities and is exquisitely sensitive to radial accelerations of the target, allowing it to detect motion in any direction. It is complementary to conventional Doppler-sensing moving target indicators, which can sense only the radial velocity of rapidly moving targets.     

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.     

Low threshold particle arrays

While atmospheric Cherenkov telescopes have a small field of view and a small duty fraction, arrays of particle detectors on ground have a 1 sr field of view and a 100% duty fraction. On the other hand, particle detector arrays have a much higher energy threshold and an inferior hadron rejection as compared to Cherenkov telescopes. Low threshold particle detector arrays would have potential advantages over Cherenkov telescopes in the search for episodic or unexpected sources of gamma rays in the multi-TeV energy range. Ways to improve the threshold and hadron rejection of arrays are shown, based on existing technology for the timing method (with scintillator or water Cherenkov counters) and the tracking method (with tracking detectors). The performance that could be achieved is shown by examples for both methods. At mountain altitude (about 4000 m or above) an energy threshold close to 1 TeV could be achieved. For any significant reduction of the hadronic background by selecting muon-poor showers a muon detection area of at least 1000 m² is required, even for a compact array.     

Three-dimensional cosmic-ray simulations: Heliographic latitude and current-sheet tilt

We present the results from a study of the variations of the cosmic-ray intensity with time, heliographic latitude, and longitude, and for varying interplanetary conditions, using our three-dimensional, time-dependent computer code for cosmic-ray transport in the heliosphere. Our code also produces a solar-wind and interplanetary magnetic field (IMF) configuration which is compared with observations. Because of the fully threedimensional nature of the model calculations, we are able to model time variations which would be expected to be observed along Ulysses's trajectory as it moves to high latitudes. In particular we can model the approximately 13-and 26-day solar-rotation induced variations in cosmic rays, solar wind and IMF, as a function of increasing heliographic latitude, as one moves poleward of the interplanetary current sheet. Our preliminary model results seem to be in general form quite similar to published data, but depend on the physical parameters used such as cosmic-ray diffusion coefficients, boundary conditions, and the nature of the solar wind and IMF and current sheet.     

Robust algorithm for combating look direction error problems

A simple and fast zero tracking algorithm for adaptive arrays with large look direction errors is presented and investigated. Basically, the algorithm is based on adjusting the complex zeroes of a power inversion array in a time-multiplexed manner to track all the sources in the environment. To preserve the desired signal which is supposed to be closest to the look direction of 0°, the algorithm removes the zero with the shortest distance to e^j0 so that the directional response consists of only nulls steered at the jammers. When compared with the least mean square (LMS) algorithm employing zeroth and first-order look direction constraints, the new algorithm has about the same implementation complexity, is considerably faster, and possesses a much better signal-to-noise ratio (SNR) performance when the look direction is erroneous     

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.