Analytic Method for Computing Instrument Pointing Jitter

A new method of calculating the root-mean-square (rms) pointing jitter of a scientific instrument (e.g., a camera, radar antenna, or telescope) is introduced based on a state-space concept. In comparison with the prior method of calculating the rms pointing jitter, the present method involves significantly less computation. The rms pointing jitter of an instrument (the square root of the jitter variance shown in the figure) is an important physical quantity which impacts the design of the instrument, its actuators, controls, sensory components, and sensor- output-sampling circuitry. Using the Sirlin, San Martin, and Lucke definition of pointing jitter, the prior method of computing the rms pointing jitter involves a frequency-domain integral of a rational polynomial multiplied by a transcendental weighting function, necessitating the use of numerical-integration techniques. In practice, numerical integration complicates the problem of calculating the rms pointing error. In contrast, the state-space method provides exact analytic expressions that can be evaluated without numerical integration

New Evidence on Sex Segregation and Sex Differences in Wages from Matched Employee-Employer Data

We assemble a new matched employer-employee data set covering essentially all industries and occupations across all regions of the U.S. We use this data set to re-examine the question of the relative contributions to the overall sex gap in wages of sex segregation vs. wage differences by sex within occupation, industry, establishment, and occupation-establishment cells. This new data set is especially useful because earlier research on this topic relied on data sets that covered only a narrow range of industries, occupations, or regions. Our results indicate that a sizable fraction of the sex gap in wages is accounted for by the segregation of women into lower-paying occupations, industries, establishments, and occupations within establishments. Nonetheless, a substantial part of the sex gap in wages remains attributable to the individual's sex. This latter finding contrasts sharply with the conclusions of previous research (especially Groshen, 1991), which indicated that sex segregation accounted for essentially all of the sex wage gap. Further research into the sources of within-establishment within-occupation sex wage differences is therefore much more important than previously thought.

Reduced-Order Kalman Filtering for Processing Relative Measurements

A study in Kalman-filter theory has led to a method of processing relative measurements to estimate the current state of a physical system, using less computation than has previously been thought necessary. As used here, relative measurements signifies measurements that yield information on the relationship between a later and an earlier state of the system. An important example of relative measurements arises in computer vision: Information on relative motion is extracted by comparing images taken at two different times. Relative measurements do not directly fit into standard Kalman filter theory, in which measurements are restricted to those indicative of only the current state of the system. One approach heretofore followed in utilizing relative measurements in Kalman filtering, denoted state augmentation, involves augmenting the state of the system at the earlier of two time instants and then propagating the state to the later time instant.While state augmentation is conceptually simple, it can also be computationally prohibitive because it doubles the number of states in the Kalman filter. When processing a relative measurement, if one were to follow the state-augmentation approach as practiced heretofore, one would find it necessary to propagate the full augmented state Kalman filter from the earlier time to the later time and then select out the reduced-order components. The main result of the study reported here is proof of a property called reduced-order equivalence (ROE). The main consequence of ROE is that it is not necessary to augment with the full state, but, rather, only the portion of the state that is explicitly used in the partial relative measurement. In other words, it suffices to select the reduced-order components first and then propagate the partial augmented state Kalman filter from the earlier time to the later time; the amount of computation needed to do this can be substantially less than that needed for propagating the full augmented Kalman state filter

Combining Multiple Gyroscope Outputs for Increased Accuracy

A proposed method of processing the outputs of multiple gyroscopes to increase the accuracy of rate (that is, angular-velocity) readings has been developed theoretically and demonstrated by computer simulation. Although the method is applicable, in principle, to any gyroscopes, it is intended especially for application to gyroscopes that are parts of microelectromechanical systems (MEMS). The method is based on the concept that the collective performance of multiple, relatively inexpensive, nominally identical devices can be better than that of one of the devices considered by itself. The method would make it possible to synthesize the readings of a single, more accurate gyroscope (a virtual gyroscope) from the outputs of a large number of microscopic gyroscopes fabricated together on a single MEMS chip. The big advantage would be that the combination of the MEMS gyroscope array and the processing circuitry needed to implement the method would be smaller, lighter in weight, and less power-hungry, relative to a conventional gyroscope of equal accuracy. The method (see figure) is one of combining and filtering the digitized outputs of multiple gyroscopes to obtain minimum-variance estimates of rate. In the combining-and-filtering operations, measurement data from the gyroscopes would be weighted and smoothed with respect to each other according to the gain matrix of a minimum- variance filter. According to Kalman-filter theory, the gain matrix of the minimum-variance filter is uniquely specified by the filter covariance, which propagates according to a matrix Riccati equation. The present method incorporates an exact analytical solution of this equation

Extended Horizon Liftings for Periodic Gain Adjustments in Control Systems, and for Equalization of Communication Channels

Periodic gain adjustment in plants of irreducible order, n, or for equalization of communications channels is effected in such a way that the plant (system) appears to be minimum phase by choosing a horizon time N greater then n of liftings in periodic input and output windows Pu and Py, respectively, where N is an integer chosen to define the extent (length) of each of the windows Pu and Py, and n is the order of an irreducible input/output plant. The plant may be an electrical, mechanical or chemical system, in which case output tracking (OT) is carried out for feedback control or a communication channel, in which case input tracking (IT) is carried out. Conditions for OT are distinct from IT in terms of zero annihilation, namely for OT and of IT, where the OT conditions are intended for gain adjustments in the control system, and IT conditions are intended for equalization for communication channels

Extended horizon lifting for periodic gain adjustment in control systems, and for equalization of communication channels

Periodic gain adjustment in plants of irreducible order, n, or for equalization of communications channels is effected in such a way that the plant (system) appears to be minimum phase by choosing a horizon time N is greater than n of liftings in periodic input and output windows rho sub u and rho sub y, respectively, where N is an integer chosen to define the extent (length) of each of the windows rho sub u and rho sub y, and n is the order of an irreducible input/output plant. The plant may be an electrical, mechanical, or chemical system, in which case output tracking (OT) is carried out for feedback control or a communication channel, in which case input tracking (IT) is performed. Conditions for OT are distinct from IT in terms of zero annihilation, namely H(sub s)H(sub s)(sup +) = I for OT and H(sub s)H(sub s)(sup +) = I of IT, where the OT conditions are intended for gain adjustments in the control system, and IT conditions are intended for equalization for communication channels

Kalman Filter for Calibrating a Telescope Focal Plane

The instrument-pointing frame (IPF) Kalman filter, and an algorithm that implements this filter, have been devised for calibrating the focal plane of a telescope. As used here, calibration signifies, more specifically, a combination of measurements and calculations directed toward ensuring accuracy in aiming the telescope and determining the locations of objects imaged in various arrays of photodetectors in instruments located on the focal plane. The IPF Kalman filter was originally intended for application to a spaceborne infrared astronomical telescope, but can also be applied to other spaceborne and ground-based telescopes. In the traditional approach to calibration of a telescope, (1) one team of experts concentrates on estimating parameters (e.g., pointing alignments and gyroscope drifts) that are classified as being of primarily an engineering nature, (2) another team of experts concentrates on estimating calibration parameters (e.g., plate scales and optical distortions) that are classified as being primarily of a scientific nature, and (3) the two teams repeatedly exchange data in an iterative process in which each team refines its estimates with the help of the data provided by the other team. This iterative process is inefficient and uneconomical because it is time-consuming and entails the maintenance of two survey teams and the development of computer programs specific to the requirements of each team. Moreover, theoretical analysis reveals that the engineering/ science iterative approach is not optimal in that it does not yield the best estimates of focal-plane parameters and, depending on the application, may not even enable convergence toward a set of estimates

State-Estimation Algorithm Based on Computer Vision

An algorithm and software to implement the algorithm are being developed as means to estimate the state (that is, the position and velocity) of an autonomous vehicle, relative to a visible nearby target object, to provide guidance for maneuvering the vehicle. In the original intended application, the autonomous vehicle would be a spacecraft and the nearby object would be a small astronomical body (typically, a comet or asteroid) to be explored by the spacecraft. The algorithm could also be used on Earth in analogous applications -- for example, for guiding underwater robots near such objects of interest as sunken ships, mineral deposits, or submerged mines. It is assumed that the robot would be equipped with a vision system that would include one or more electronic cameras, image-digitizing circuitry, and an imagedata- processing computer that would generate feature-recognition data products

FuzzObserver

Fuzzy Feature Observation Planner for Small Body Proximity Observations (FuzzObserver) is a developmental computer program, to be used along with other software, for autonomous planning of maneuvers of a spacecraft near an asteroid, comet, or other small astronomical body. Selection of terrain features and estimation of the position of the spacecraft relative to these features is an essential part of such planning. FuzzObserver contributes to the selection and estimation by generating recommendations for spacecraft trajectory adjustments to maintain the spacecraft's ability to observe sufficient terrain features for estimating position. The input to FuzzObserver consists of data from terrain images, including sets of data on features acquired during descent toward, or traversal of, a body of interest. The name of this program reflects its use of fuzzy logic to reason about the terrain features represented by the data and extract corresponding trajectory-adjustment rules. Linguistic fuzzy sets and conditional statements enable fuzzy systems to make decisions based on heuristic rule-based knowledge derived by engineering experts. A major advantage of using fuzzy logic is that it involves simple arithmetic calculations that can be performed rapidly enough to be useful for planning within the short times typically available for spacecraft maneuvers