Beamspace ML bearing estimation incorporating low-angle geometry

A problem in low-angle radar tracking, namely, bearing estimation in the presence of a strong specular multipath component that arrives within the beamwidth of the direct path signal, is studied. Three-dimensional beamspace domain maximum likelihood (3D-BDML) is a computationally simple ML bearing estimation algorithm applicable in this scenario which operates in a 3-D beamspace. A variation of 3D-BDML incorporating the multipath geometry as a priori information is presented. In symmetric 3D-BDML the pointing angle of the center beam is equal to the bisector angle between the direct path ray and the image ray, which may be estimated a priori given only the radar height and the target range. The effect of the inclusion of a priori information on the performance of 3D-BDML is analyzed in terms of the dependence on the relative phase difference between the direct and specular path signals, the sensitivity to error in the bisector angle estimate, and the results of operation when no specular multipath component is present in the data. In addition, computationally simple schemes for coherently incorporating multifrequency data into 3D-BDML are investigated     

Computation of the circular error probability integral

The author describes a simplified derivation of the representation of the circular error probability (CEP) integral, which is the integral over a disk centered at the origin of a zero mean two-dimensional Gaussian random variable, as a one-dimensional integral. In addition, two series are presented which can be used to compute efficiently the CEP integral. The domain of applicability of the series and methods for acceleration of the convergence of these series are discussed. The integral occurs in the evaluation of communication and radar signals, and in other statistical applications.<>     

The relevant atomic data

The current status of the theoretical methods for producing the relevant atomic data is surveyed.Proceedings of the Conference Solar Physics from Space, held at at the Swiss Federal Institute of Technology Zurich (ETHZ), 11–14 November 1980.     

Leading Edge Estimation Errors

The leading edge estimator (LEE) of a pulse signal is defined as the instant at which a filtered version of the received noisy signal passes a preset threshold. A rigorous analysis for a rectangular pulse model of the signal results in an exact probability density function for the LEE, valid within the time interval of the leading edge of the filtered pulse. Possible occurrence of the threshold crossing outside of this interval is considered to be an anomalous estimate, since it leads to a gross error in comparison with the regular cases. It is found that the density function of the LEE error is asymmetrical and therefore biased, that the probability PA of anomalous estimation increases with the filter bandwidth, thus setting a well definable limit to the latter and that, for prespecified PA, the minimum bias and variance are proportional, respectively, to R-1 and R-2, minima being obtained by allowing for the largest bandwidth compatible with PA. On the other hand, for given bandwidth the variance decreases only as R-1. Here R is the signal-to-noise energy ratio. Results are presented in form of parameterized graphs.     

Cross Sections and Radar Equation for Nonlinear Scatterers

The nonlinear system concepts of nonlinear transfer functions are extended to nonlinear cross sections which may be used to quantitatively describe the characteristics of a nonlinear scatter. The concept of nonlinear cross sections is used to generalize the radar equation for nonlinear scattering objects.     

Radar Performance Review in Clear and Jamming Environments

The performance of electronically scanned radar systems is evaluated for clear and barrage jamming environments. Radar figures of merit in jamming are derived for search and track modes and are directly related to antenna pattern relative sidelobe levels. A random sidelobe model is analyzed with various numbers of independent jammers. Probability distributions of detection probability are derived to determine detection performance versus average jamming level and number of jammers.     

Observations of the Acceleration of Polar Solar Wind Near Solar Maximum

In a previous paper (Tappin et al., 1999) we used cross-correlation analysis of high-cadence observations with the LASCO coronagraphs to trace the acceleration of the solar wind at low latitudes. In this paper we present a similar analysis carried out over the North pole of the Sun. The observations which were made in March 2000 with the C3 coronagraph show low bulk flow speeds (comparable to or lower than those seen at the equator in early 1998). We observe the acceleration continuing to the edge of the C3 field of view at about 30 R _⊙. We also observe, as at low latitude, a high-speed tail but now reaching out well beyond 2000 km s⁻¹. We do not see a clear signature of a fast polar bulk flow. We therefore conclude that at this phase of the solar cycle, any fast bulk flow occupies only a small part of the line of sight and is therefore overwhelmed by the denser slow solar wind in these observations. We also show that the fast component is consistent with observed solar wind speeds at 1 AU. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Heliospheric Magnetic Field at Solar Maximum: Ulysses Observations

At solar maximum, the large-scale structure of the heliospheric magnetic field (HMF) reflects the complexity of the Sun's coronal magnetic fields. The corona is characterised by mostly closed magnetic structures and short-lived, small coronal holes. The axis of the Sun's dipole field is close to the solar equator; there are also important contributions from the higher order terms. This complex and variable coronal magnetic configuration leads to a much increased variability in the HMF on all time scales, at all latitudes. The transition from solar minimum to solar maximum conditions, as reflected in the HMF, is described, as observed by Ulysses during its passage to high southern heliolatitudes. The magnetic signatures associated with the interaction regions generated by short-lived fast solar wind streams are presented, together with the highly disordered period in mid-1999 when there was a considerable reorganisation in coronal structures. The magnetic sector structure at high heliolatitudes shows, from mid-1999, a recognisable two-sector structure, corresponding to a highly inclined Heliospheric Current Sheet. A preliminary investigation of the radial component of the magnetic field indicates that it remains, on average, constant as a function of heliolatitude. Intervals of highly Alfvénic fluctuations in the rarefaction regions trailing the interaction regions have been, even if intermittently, identified even close to solar maximum. This revised version was published online in August 2006 with corrections to the Cover Date.     

The importance of anisotropic interstellar turbulence and molecular-cloud magnetic mirrors for galactic cosmic-ray propagation

Recent studies suggest that when magnetohydrodynamic (MHD) turbulence is excited by stirring a plasma at large scales, the cascade of energy from large to small scales is anisotropic, in the sense that small-scale fluctuations satisfy the inequality k k , where k and k are, respectively, the components of a fluctuations wave vector and to the background magnetic field. Such anisotropic fluctuations are very inefficient at scattering cosmic rays. Results based on the quasilinear approximation for scattering of cosmic rays by anisotropic MHD turbulence are presented and explained. The important role played by molecular-cloud magnetic mirrors in confining and isotropizing cosmic rays when scattering is weak is also discussed.