Kalman filtering with state equality constraints

Kalman filters are commonly used to estimate the states of a dynamic system. However, in the application of Kalman filters there is often known model or signal information that is either ignored or dealt with heuristically. For instance, constraints on state values (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. A rigorous analytic method of incorporating state equality constraints in the Kalman filter is developed. The constraints may be time varying. At each time step the unconstrained Kalman filter solution is projected onto the state constraint surface. This significantly improves the prediction accuracy of the filter. The use of this algorithm is demonstrated on a simple nonlinear vehicle tracking problem     

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.     

Cross-correlation properties of algebraically constructed Costasarrays

The problem of determining the cross-correlation properties of signals based on algebraically constructed Costas arrays is addressed by examining the discrete cross-correlation of the algebraically constructed Costas arrays for a given construction and dimension. Finding two arrays that minimally correlate implies that the signals based on these arrays also minimally correlate. The properties of finite fields are reviewed, and the major algebraic constructions for Costas arrays are presented, i.e. the Welch construction and the Golomb construction. The discrete cross-correlation properties of the Costas arrays are derived for arrays of the same dimension derived from the same construction. The use of Costas arrays in the signal design problem is discussed, and examples are given to show the cross-correlation of the signals based on the algebraically constructed arrays     

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     

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.     

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.     

An Overview of the Fast Auroral SnapshoT (FAST) Satellite

The FAST satellite is a highly sophisticated scientific satellite designed to carry out in situ measurements of acceleration physics and related plasma processes associated with the Earth's aurora. Initiated and conceptualized by scientists at the University of California at Berkeley, this satellite is the second of NASA's Small Explorer Satellite program designed to carry out small, highly focused, scientific investigations. FAST was launched on August 21, 1996 into a high inclination (83°) elliptical orbit with apogee and perigee altitudes of 4175 km and 350 km, respectively. The spacecraft design was tailored to take high-resolution data samples (or `snapshots') only while it crosses the auroral zones, which are latitudinally narrow sectors that encircle the polar regions of the Earth. The scientific instruments include energetic electron and ion electrostatic analyzers, an energetic ion instrument that distinguishes ion mass, and vector DC and wave electric and magnetic field instruments. A state-of-the-art flight computer (or instrument data processing unit) includes programmable processors that trigger the burst data collection when interesting physical phenomena are encountered and stores these data in a 1 Gbit solid-state memory for telemetry to the Earth at later times. The spacecraft incorporates a light, efficient, and highly innovative design, which blends proven sub-system concepts with the overall scientific instrument and mission requirements. The result is a new breed of space physics mission that gathers unprecedented fields and particles observations that are continuous and uninterrupted by spin effects. In this and other ways, the FAST mission represents a dramatic advance over previous auroral satellites. This paper describes the overall FAST mission, including a discussion of the spacecraft design parameters and philosophy, the FAST orbit, instrument and data acquisition systems, and mission operations.     

Receiver antenna scan rate requirements needed to implement pulsechasing in a bistatic radar receiver

Pulse chasing is a technique implemented by a bistatic or multistatic radar system that allows rapid and efficient search of a desired volume of space whereby the receiving antenna is made to follow or “chase” the transmitted pulse as it travels radially outward from the transmitter antenna. An expression for receiver antenna scan rate requirements is derived that corrects an error in the prior literature. The results give significantly reduced scan rates in the forward scatter region near the baseline showing that pulse chasing is more easily implemented using conventional analog beamformer phased array technology than was suggested by prior work     

Performance limits of sensor-scheduling strategies in electronic support

The case is considered in which a frequency-agile receiver (FAR) for electronic support (ES) attempts to intercept radar emissions over a wide search bandwidth. It was recently shown [1,2] that a random strategy exists in which the expected intercept time can be made arbitrarily close to linear as a function of the scan period of the radar. Can a deterministic strategy be devised in which a similar linear relationship exists for the maximum intercept time? By applying the celebrated arithmetic results of van der Waerden [3] and Szemeredi [4], we show that no such strategy is possible.