Geometric View of Measurement Errors

The slope of the best fit line from minimizing the sum of the squared oblique errors is the root of a polynomial of degree four. This geometric view of measurement errors is used to give insight into the performance of various slope estimators for the measurement error model including an adjusted fourth moment estimator introduced by Gillard and Iles (2005) to remove the jump discontinuity in the estimator of Copas (1972). The polynomial of degree four is associated with a minimun deviation estimator. A simulation study compares these estimators showing improvement in bias and mean squared error

Evaluation of servo, geometric and dynamic error sources on five axis high-speed machine tool

Many sources of errors exist in the manufacturing process of complex shapes. Some approximations occur at each step from the design geometry to the machined part. The aim of the paper is to present a method to evaluate the effect of high speed and high dynamic load on volumetric errors at the tool center point. The interpolator output signals and the machine encoder signals are recorded and compared to evaluate the contouring errors resulting from each axis follow-up error. The machine encoder signals are also compared to the actual tool center point position as recorded with a non-contact measuring instrument called CapBall to evaluate the total geometric errors. The novelty of the work lies in the method that is proposed to decompose the geometric errors in two categories: the quasi-static geometric errors independent from the speed of the trajectory and the dynamic geometric errors, dependent on the programmed feed rate and resulting from the machine structure deflection during the acceleration of its axes. The evolution of the respective contributions for contouring errors, quasi-static geometric errors and dynamic geomet- ric errors is experimentally evaluated and a relation between programmed feed rate and dynamic errors is highlighted.Comment: 13 pages; International Journal of Machine Tools and Manufacture (2011) pp XX-X

Measurement Errors and their Propagation in the Registration of Remote Sensing Images (?)

Reference control points (RCPs) used in establishing the regression model in the registration or geometric correction of remote sensing images are generally assumed to be ?perfect?. That is, the RCPs, as explanatory variables in the regression equation, are accurate and the coordinates of their locations have no errors. Thus ordinary least squares (OLS) estimator has been applied extensively to the registration or geometric correction of remotely sensed data. However, this assumption is often invalid in practice because RCPs always contain errors. Moreover, the errors are actually one of the main sources which lower the accuracy of geometric correction of an uncorrected image. Under this situation, the OLS estimator is biased. It cannot handle explanatory variables with errors and cannot propagate appropriately errors from the RCPs to the corrected image. Therefore, it is essential to develop new feasible methods to overcome such a problem. In this paper, we introduce the consistent adjusted least squares (CALS) estimator and propose a relaxed consistent adjusted least squares (RCALS) method, with the latter being more general and flexible, for geometric correction or registration. These estimators have good capability in correcting errors contained in the RCPs, and in propagating appropriately errors of the RCPs to the corrected image with and without prior information. The objective of the CALS and our proposed RCALS estimators is to improve the accuracy of measurement value by weakening the measurement errors. The validity of the CALS and RCALS estimators are first demonstrated by applying them to perform geometric corrections of controlled simulated images. The conceptual arguments are further substantiated by a real-life example. Compared to the OLS estimator, the CALS and RCALS estimators give a superior overall performances in estimating the regression coefficients and variance of measurement errors. Keywords: error propagation, geometric correction, ordinary least squares, registration, relaxed consistent adjusted least squares, remote sensing images.

Geometric quantum gates robust against stochastic control errors

We analyze a scheme for quantum computation where quantum gates can be continuously changed from standard dynamic gates to purely geometric ones. These gates are enacted by controlling a set of parameters that are subject to unwanted stochastic fluctuations. This kind of noise results in a departure from the ideal case that can be quantified by a gate fidelity. We find that the maximum of this fidelity corresponds to quantum gates with a vanishing dynamical phase.Comment: 4 pager

Environment-assisted holonomic quantum maps

Holonomic quantum computation uses non-Abelian geometric phases to realize error resilient quantum gates. Nonadiabatic holonomic gates are particularly suitable to avoid unwanted decoherence effects, as they can be performed at high speed. By letting the computational system interact with a structured environment, we show that the scope of error resilience of nonadiabatic holonomic gates can be widened to include systematic parameter errors. Our scheme maintains the geometric properties of the evolution and results in an environment-assisted holonomic quantum map that can mimic the effect of a holonomic gate. We demonstrate that the sensitivity to systematic errors can be reduced in a proof-of-concept spin-bath model.Comment: New figure added. Journal reference adde

Geometric Quantum Gates, Composite Pulses, and Trotter-Suzuki Formulas

We show that all geometric quantum gates (GQG's in short), which are quantum gates only with geometric phases, are robust against control field strength errors. As examples of this observation, we show (1) how robust composite rf-pulses in NMR are geometrically constructed and (2) a composite rf-pulse based on Trotter-Suzuki Formulas is a GQG.Comment: 4 pages, no figure

Universal quantum computation by holonomic and nonlocal gates with imperfections

We present a nonlocal construction of universal gates by means of holonomic (geometric) quantum teleportation. The effect of the errors from imperfect control of the classical parameters, the looping variation of which builds up holonomic gates, is investigated. Additionally, the influence of quantum decoherence on holonomic teleportation used as a computational primitive is studied. Advantages of the holonomic implementation with respect to control errors and dissipation are presented.Comment: 5 pages, 2 figures, REVTEX, title changed, typos correcte

Comparative assessment of LANDSAT-4 MSS and TM data quality for mapping applications in the southeast

The initial objectives of analyses of the MSS data are two-fold: (1) to evaluate the geodetic accuracy of CCT-P data of the test sites; and (2) to improve the geodetic accuracy by additional processing if the original data either do not meet pre-launch specifications or mapping requirements. The location of 45 ground control points (GCP) digitized from 35 U.S. Geological Survey 1:24,000 scale quadrangles (UTM coordinates) were identified in terms of pixel and scan line values. These 46 points are used to establish UTM position error vector distributions in the scene. As an initial check on the geometric reliability of the MSS data, 28 well-distributed GCPs were input to a program which compares the scaled image distances between all possible point pairs with the corresponding map distances and computes the distance differences; that is, the relative positional errors. The relative errors obtained from initial computations averaged about +/- 200 m. These errors could result from a number of sources, including misidentification of GCP locations, UTM coordinate errors introduced by the map digitizing process or errors resulting from data acquisition and geometric processing