G. M. Keiser

Optimal Recursive Iterative Algorithm for Discrete Nonlinear Least-Squares Estimation

The estimation algorithm developed offers an alternative to standard recursive nonlinear estimators such as the extended Kalman filter and the iterated extended Kalman filter. The algorithm, which is developed from a quadratic cost function basis, splits the problem of cost function minimization into a linear first step and a nonlinear second step by defining new first-step states that are nonlinear combinations of the unknown states. Estimates of the firststep states are obtained by minimizing the first-step cost function using a Kalman filter formulation. Estimates of the unknown, or second-step, states are obtained by minimizing the second-step cost function using an iterative Gauss-Newton algorithm. The two-step estimator is shown to be optimal for static problems in which the time variation of the measurement equation can be separated from the unknowns. This method is then generalized by approximating the nonlinearity as a perturbation of the dynamic update, while keeping the measurement cost function the same. In contrast, the extended Kalman filter and the iterated extended Kalman filter linearize the measurement cost function, resulting in suboptimal estimates. Two example applications confirm these analytical results.

The gravity-probe-b relativity gyroscope experiment: Development of the prototype flight instrument

The Gravity-Probe-B Relativity Gyroscope Experiment (GP-B) will measure the geodetic and frame-dragging precession rates of gyroscopes in a 650 km high polar orbit about the earth. The goal is to measure these two effects, which are predicted by Einsteins General Theory of Relativity, to 0.01% (geodetic) and 1% (frame-dragging). This paper presents the development progress for full-size prototype flight hardware including the gyroscopes, gyro readout and magnetic shielding system, and an integrated ground test instrument. Results presented include gyro rotor mass-unbalance values (15–86 nm) due the thickness variations of the thin niobium coating on the rotor, interior sphericities (163–275 nm peak-to-valley) of fused-quartz gyro housings produced by tumble lapping, gyro precession rates (gyroscopes at 5 K) which imply low mass-unbalance components parallel to the gyro axis (23–62 nm), and demonstration of a magnetic shielding factor of 2×1010 for the gyro readout system with one shielding component missing (the gyro rotor). All of these results are at or near flight requirements for the GP-B Science Mission, which is expected to be launched in 1995.

Charge measurement and control for the Gravity Probe B gyroscopes

We describe a technique based on photoemission for controlling the charge of the Gravity Probe B electrostatically suspended gyroscopes, and three methods for measuring this charge. Charging is caused by cosmic radiation in orbit and by enhanced field emission in ground testing. Errors induced by disturbing torques require the potential of the gyroscope to be smaller than 15 mV (15 pC) during the space experiment. The disturbing drift rate produced by measuring and controlling the charge in orbit is smaller than 10−13 deg/h, as compared with the 10−11 deg/h systematic drift rate of the gyroscope. The charge control technique is based on ultraviolet photoemission of electrons from both the gyroscope and a charge control electrode on the gyroscope housing. We demonstrate the effectiveness of this method in ground testing and therefore its suitability for the space experiment. Calculations indicate that heating by absorbed photons is, in the worst case, smaller than 1 nW and thus not a problem for the experi...

The Gravity Probe B test of general relativity

The Gravity Probe B mission provided two new quantitative tests of Einsteins theory of gravity, general relativity (GR), by cryogenic gyroscopes in Earths orbit. Data from four gyroscopes gave a geodetic drift-rate of −6601.8 ± 18.3 marc-s yr−1 and a frame-dragging of −37.2 ± 7.2 marc-s yr−1, to be compared with GR predictions of −6606.1 and −39.2 marc-s yr−1 (1 marc-s = 4.848 × 10−9 radians). The present paper introduces the science, engineering, data analysis, and heritage of Gravity Probe B, detailed in the accompanying 20 CQG papers.

Disturbance reduction system: testing technology for drag-free operation

The Disturbance Reduction System (DRS) is designed to demonstrate technology required for future gravity missions, including the planned LISA gravitational-wave observatory, and for precision formation-flying missions. The DRS is based on a freely floating test mass contained within a spacecraft that shields the test mass from external forces. The spacecraft position will be continuously adjusted to stay centered about the test mass, essentially flying in formation with the test mass. Any departure of the test mass from a gravitational trajectory is characterized as acceleration noise, resulting from unwanted forces acting on the test mass. The DRS goal is to demonstrate a level of acceleration noise more than four orders of magnitude lower than previously demonstrated in space. The DRS will consist of an instrument package and a set of microthrusters, which will be attached to a suitable spacecraft. The instrument package will include two Gravitational Reference Sensors comprised of a test mass within a reference housing. The spacecraft position will be adjusted using colloidal microthrusters, which are miniature ion engines that provide continuous thrust with a range of 1-20 mN with resolution of 0.1 mN. The DRS will be launched in 2007 as part of the ESA SMART-2 spacecraft. The DRS is a project within NASAs New Millennium Program.

Development of the Gravity Probe B flight mission

Abstract Gravity Probe B is an experiment to measure the geodetic and frame-dragging precessions, relative to the “fixed” “stars”, of a gyroscope placed in a 650 km altitude polar orbit about the earth. For Einsteins general relativity, the precessions are calculated to be 6.6 arcsec/yr for the geodetic precession and 0.042 arcsec/yr for the frame-dragging precession. The goal of the experiment is to measure these precessions to better than 0.01% and 1%, respectively. This paper gives an overview of the experiment and a discussion of the flight hardware development and its status. This paper also includes an estimate of the geodetic and frame-dragging errors expected for the experiment.

Magnetic flux distribution on a spherical superconducting shell

Abstract We report measurements of flux distributions on superconducting spherical shells in an ambient magnetic field of 0.2±0.1 μG. The aim of these experiments is to minimize the number of flux lines trapped in the superconducting shells, an important requirement for the Gravity Probe B gyroscopes.

Gravity Probe B data analysis: II. Science data and their handling prior to the final analysis

The results of the Gravity Probe B relativity science mission published in Everitt et al (2011 Phys. Rev. Lett. 106 221101) required a rather sophisticated analysis of experimental data due to several unexpected complications discovered on-orbit. We give a detailed description of the Gravity Probe B data reduction. In the first paper (Silbergleit et al Class. Quantum Grav. 22 224018) we derived the measurement models, i.e., mathematical expressions for all the signals to analyze. In the third paper (Conklin et al Class. Quantum Grav. 22 224020) we explain the estimation algorithms and their program implementation, and discuss the experiment results obtained through data reduction. This paper deals with the science data preparation for the main analysis yielding the relativistic drift estimates.

Gravity Probe B data analysis: III. Estimation tools and analysis results

This paper provides detailed descriptions of the numerical estimation algorithms used to fit physics-based models to the data from the Gravity Probe B spacecraft, as well as the scientific results of the experiment, and the statistical and systematic uncertainties. The first paper in this series of three data analysis papers derives the mathematical expressions for the signals to be analyzed, and the second paper deals with science data acquisition and their preparation for the relativistic drift rate estimation. The data from each of the four gyroscopes are partitioned into six segments, each spanning several weeks to several months. These segments are first analyzed individually to check the validity of the mathematical models and the accuracy of the estimation routine by examining the consistency of the relativistic drift rate estimates from each of these 24 gyro-segments. Then, the drift rate estimates and uncertainties are calculated for each individual gyroscope and for the four gyroscopes combined. These results are presented and compared with each other and with the prediction of general relativity.

Gravity Probe B data analysis: I. Coordinate frames and analysis models

Gravity Probe B (GP-B) was a cryogenic, space-based experiment testing the geodetic and frame-dragging predictions of Einsteins theory of general relativity (GR) by means of gyroscopes in Earth orbit. This first of three data analysis papers reviews the GR predictions and details the models that provide the framework for the relativity analysis. In the second paper we describe the flight data and their preprocessing. The third paper covers the algorithms and software tools that fit the preprocessed flight data to the models to give the experimental results published in Everitt et al (2011 Phys. Rev. Lett. 106 221101–4).