Optimal Estimation of Several Linear Parameters in the Presence of Lorentzian Thermal Noise

In a previous article we developed an approach to the optimal (minimum variance, unbiased) statistical estimation technique for the equilibrium displacement of a damped, harmonic oscillator in the presence of thermal noise. Here, we expand that work to include the optimal estimation of several linear parameters from a continuous time series. We show that working in the basis of the thermal driving force both simplifies the calculations and provides additional insight to why various approximate (not optimal) estimation techniques perform as they do. To illustrate this point, we compare the variance in the optimal estimator that we derive for thermal noise with those of two approximate methods which, like the optimal estimator, suppress the contribution to the variance that would come from the irrelevant, resonant motion of the oscillator. We discuss how these methods fare when the dominant noise process is either white displacement noise or noise with power spectral density that is inversely proportional to the frequency ($1/f$ noise). We also construct, in the basis of the driving force, an estimator that performs well for a mixture of white noise and thermal noise. To find the optimal multi-parameter estimators for thermal noise, we derive and illustrate a generalization of traditional matrix methods for parameter estimation that can accommodate continuous data. We discuss how this approach may help refine the design of experiments as they allow an exact, quantitative comparison of the precision of estimated parameters under various data acquisition and data analysis strategies.Comment: 16 pages, 10 figures. Accepted for publication in Classical and Quantum Gravit

A radar-echo model for Mars

Researchers developed a radar-echo model for Mars based on 12.6 cm continuous wave radio transmissions backscattered from the planet. The model broadly matches the variations in depolarized and polarized total radar cross sections with longitude observed by Goldstone in 1986 along 7 degrees S. and yields echo spectra that are generally similiar to the observed spectra. Radar map units in the model include an extensive cratered uplands unit with weak depolarized echo cross sections, average thermal inertias, moderate normal refelectivities, and moderate rms slopes; the volcanic units of Tharsis, Elysium, and Amazonis regions with strong depolarized echo cross sections, low thermal inertia, low normal reflectivities, and large rms slopes; and the northern planes units with moderate to strong depolarized echo cross sections, moderate to very high thermal inertias, moderate to large normal reflectivities, and moderate rms slopes. The relevance of the model to the interpretation of radar echoes from Mars is discussed

Gypsy moth defoliation assessment: Forest defoliation in detectable from satellite imagery

The author has identified the following significant results. ERTS-1 imagery obtained over eastern Pennsylvania during July 1973, indicates that forest defoliation is detectable from satellite imagery and correlates well with aerial visual survey data. It now appears that two damage classes (heavy and moderate-light) and areas of no visible defoliation can be detected and mapped from properly prepared false composite imagery. In areas where maple is the dominant species or in areas of small woodlots interspersed with agricultural areas, detection and subsequent mapping is more difficult

Investigation of advanced navigation and guidance system concepts for all-weather rotorcraft operations

Results are presented of a survey conducted of active helicopter operators to determine the extent to which they wish to operate in IMC conditions, the visibility limits under which they would operate, the revenue benefits to be gained, and the percent of aircraft cost they would pay for such increased capability. Candidate systems were examined for capability to meet the requirements of a mission model constructed to represent the modes of flight normally encountered in low visibility conditions. Recommendations are made for development of high resolution radar, simulation of the control display system for steep approaches, and for development of an obstacle sensing system for detecting wires. A cost feasibility analysis is included

Exploring constrained quantum control landscapes

The broad success of optimally controlling quantum systems with external fields has been attributed to the favorable topology of the underlying control landscape, where the landscape is the physical observable as a function of the controls. The control landscape can be shown to contain no suboptimal trapping extrema upon satisfaction of reasonable physical assumptions, but this topological analysis does not hold when significant constraints are placed on the control resources. This work employs simulations to explore the topology and features of the control landscape for pure-state population transfer with a constrained class of control fields. The fields are parameterized in terms of a set of uniformly spaced spectral frequencies, with the associated phases acting as the controls. Optimization results reveal that the minimum number of phase controls necessary to assure a high yield in the target state has a special dependence on the number of accessible energy levels in the quantum system, revealed from an analysis of the first- and second-order variation of the yield with respect to the controls. When an insufficient number of controls and/or a weak control fluence are employed, trapping extrema and saddle points are observed on the landscape. When the control resources are sufficiently flexible, solutions producing the globally maximal yield are found to form connected `level sets' of continuously variable control fields that preserve the yield. These optimal yield level sets are found to shrink to isolated points on the top of the landscape as the control field fluence is decreased, and further reduction of the fluence turns these points into suboptimal trapping extrema on the landscape. Although constrained control fields can come in many forms beyond the cases explored here, the behavior found in this paper is illustrative of the impacts that constraints can introduce.Comment: 10 figure

Study of Chromium-Frit-Type Coatings for High-Temperature Protection of Molybdenum

The achievement of more compact and efficient power plants for aircraft is dependent, among other factors, on the perfection of heat-resisting materials that are superior to those in current use. Molybdenum is one of the high-melting metals (melting point, 4750 F). It is fairly abundant and also can be worked into many of the shapes required in modern power plants. To permit its widespread use at elevated temperatures, however, some means must first be found to prevent its rapid oxidation. The application of a protective coating is one method that might be used to achieve this goal. In the present work, a number of chromium-frit-type coatings were studied. These were bonded to molybdenum specimens by firing in controlled atmospheres to temperatures in the range of 2400 to 2700 F