Mathematic Model And Error Analysis of Moving-base Rotating Accelerometer Gravity Gradiometer

In moving-base gravity gradiometry, accelerometer mounting errors and mismatch cause a rotating accelerometer gravity gradiometer (RAGG) to besusceptible to its own motion. In this study, we comprehensively consider accelerometer mounting errors, circuit gain mismatch, accelerometer linear scale factors imbalances, accelerometer second-order error coefficients and construct three RAGG models, namely a numerical model, an analytical model, and a simplified analytical model. The analytical model and the simplified analytical model are used to interpret the error propagation mechanism and develop error compensation techniques. A multifrequency gravitational gradient simulation experiment and a dynamic simulation experiment are designed to verify the correctness of the three RAGG models; three turbulence simulation experiments are designed to evaluate the noise floor of the analytical models at different intensity of air turbulence. The mean of air turbulence is in the range of 70 to 230 mg, the noise density of the analytical model is about 0.13 Eo/sqrtHz, and that of the simplified analytical model is in the range of 0.25 to 1.24 Eo/sqrtHz. The noise density of the analytical models is far less than 7 Eo/sqrtHz, which suggests that using the error compensation techniques based on the analytical models, the turbulence threshold of survey flying may be widened from current 100 mg to 200 mg.Comment: 16 pages, 10 figure

A symptotic Bias for GMM and GEL Estimators with Estimated Nuisance Parameter

This papers studies and compares the asymptotic bias of GMM and generalized empirical likelihood (GEL) estimators in the presence of estimated nuisance parameters. We consider cases in which the nuisance parameter is estimated from independent and identical samples. A simulation experiment is conducted for covariance structure models. Empirical likelihood offers much reduced mean and median bias, root mean squared error and mean absolute error, as compared with two-step GMM and other GEL methods. Both analytical and bootstrap bias-adjusted two-step GMM estima-tors are compared. Analytical bias-adjustment appears to be a serious competitor to bootstrap methods in terms of finite sample bias, root mean squared error and mean absolute error. Finite sample variance seems to be little affected

A theory of human error

Human errors tend to be treated in terms of clinical and anecdotal descriptions, from which remedial measures are difficult to derive. Correction of the sources of human error requires an attempt to reconstruct underlying and contributing causes of error from the circumstantial causes cited in official investigative reports. A comprehensive analytical theory of the cause-effect relationships governing propagation of human error is indispensable to a reconstruction of the underlying and contributing causes. A validated analytical theory of the input-output behavior of human operators involving manual control, communication, supervisory, and monitoring tasks which are relevant to aviation, maritime, automotive, and process control operations is highlighted. This theory of behavior, both appropriate and inappropriate, provides an insightful basis for investigating, classifying, and quantifying the needed cause-effect relationships governing propagation of human error

Asymptotic bias for GMM and GEL estimators with estimated nuisance parameters

This papers studies and compares the asymptotic bias of GMM and generalized empirical likelihood (GEL) estimators in the presence of estimated nuisance parameters. We consider cases in which the nuisance parameter is estimated from independent and identical samples. A simulation experiment is conducted for covariance structure models. Empirical likelihood offers much reduced mean and median bias, root mean squared error and mean absolute error, as compared with two-step GMM and other GEL methods. Both analytical and bootstrap bias-adjusted two-step GMM estimators are compared. Analytical bias-adjustment appears to be a serious competitor to bootstrap methods in terms of finite sample bias, root mean squared error and mean absolute error. Finite sample variance seems to be little affected.

Non-averaged regularized formulations as an alternative to semi-analytical orbit propagation methods

This paper is concerned with the comparison of semi-analytical and non-averaged propagation methods for Earth satellite orbits. We analyse the total integration error for semi-analytical methods and propose a novel decomposition into dynamical, model truncation, short-periodic, and numerical error components. The first three are attributable to distinct approximations required by the method of averaging, which fundamentally limit the attainable accuracy. In contrast, numerical error, the only component present in non-averaged methods, can be significantly mitigated by employing adaptive numerical algorithms and regularized formulations of the equations of motion. We present a collection of non-averaged methods based on the integration of existing regularized formulations of the equations of motion through an adaptive solver. We implemented the collection in the orbit propagation code THALASSA, which we make publicly available, and we compared the non-averaged methods to the semi-analytical method implemented in the orbit propagation tool STELA through numerical tests involving long-term propagations (on the order of decades) of LEO, GTO, and high-altitude HEO orbits. For the test cases considered, regularized non-averaged methods were found to be up to two times slower than semi-analytical for the LEO orbit, to have comparable speed for the GTO, and to be ten times as fast for the HEO (for the same accuracy). We show for the first time that efficient implementations of non-averaged regularized formulations of the equations of motion, and especially of non-singular element methods, are attractive candidates for the long-term study of high-altitude and highly elliptical Earth satellite orbits.Comment: 33 pages, 10 figures, 7 tables. Part of the CMDA Topical Collection on "50 years of Celestial Mechanics and Dynamical Astronomy". Comments and feedback are encourage