Rigid Body Rate Inference from Attitude Variation

In this paper we research the extraction of the angular rate vector from attitude information without differentiation, in particular from quaternion measurements. We show that instead of using a Kalman filter of some kind, it is possible to obtain good rate estimates, suitable for spacecraft attitude control loop damping, using simple feedback loops, thereby eliminating the need for recurrent covariance computation performed when a Kalman filter is used. This considerably simplifies the computations required for rate estimation in gyro-less spacecraft. Some interesting qualities of the Kalman filter gain are explored, proven and utilized. We examine two kinds of feedback loops, one with varying gain that is proportional to the well known Q matrix, which is computed using the measured quaternion, and the other type of feedback loop is one with constant coefficients. The latter type includes two kinds; namely, a proportional feedback loop, and a proportional-integral feedback loop. The various schemes are examined through simulations and their performance is compared. It is shown that all schemes are adequate for extracting the angular velocity at an accuracy suitable for control loop damping

On the Extraction of Angular Velocity from Attitude Measurements

In this paper we research the extraction of the angular rate vector from attitude information without differentiation, in particular from quaternion measurements. We show that instead of using a Kalman filter of some kind, it is possible to obtain good rate estimates, suitable for spacecraft attitude control loop damping, using simple feedback loops, thereby eliminating the need for recurrent covariance computation performed when a Kalman filter is used. This considerably simplifies the computations required for rate estimation in gyro-less spacecraft. Some interesting qualities of the Kalman filter gain are explored, proven and utilized. We examine two kinds of feedback loops, one with varying gain that is proportional to the well known Q matrix, which is computed using the measured quaternion, and the other type of feedback loop is one with constant coefficients. The latter type includes two kinds; namely, a proportional feedback loop, and a proportional-integral feedback loop. The various schemes are examined through simulations and their performance is compared. It is shown that all schemes are adequate for extracting the angular velocity at an accuracy suitable for control loop damping

Zero modes in a system of Aharonov-Bohm fluxes

We study zero modes of two-dimensional Pauli operators with Aharonov--Bohm fluxes in the case when the solenoids are arranged in periodic structures like chains or lattices. We also consider perturbations to such periodic systems which may be infinite and irregular but they are always supposed to be sufficiently scarce

The 8 year functional and symptomatic outcome of first episode psychosis (FEP)

The study purpose is to examine the 8-year functional and symptomatic outcome of a FEP cohort of 800 patients in addition to the course patterns of psychosis over time. The design is a naturalistic, prospective, longitudinal, 8-year follow-up study with multiple follow- up time points, on a representative multidiagnostic cohort of 800 patients with FEP from the Early Psychosis Prevention and Intervention Centre, which is a frontline public mental health service and its precursor service in Melbourne, Australia. Recruitment is ongoing. The preliminary results which follow concern the 470 subjects who have been interviewed to date. At 8-year outcome, analyses indicate that 74% remain unmarried, 54% are either working, studying or are homemakers. Mean scores on quality of life and social functioning measures indicate functioning in the good range. 75% are currently receiving psychiatric treatment, however 45% of these were being treated in the private health sector suggesting less severe illness and better functioning. Those taking an antipsychotic were on a CPZ equivalent mean low dose of 303mg. In terms of psychiatric hospital admission, 60% have not been admitted in the most recent two years and the mean number of admissions over the 8-year period was two. 47% have not been psychotic in the most recent 2 years and one quarter never had another psychotic episode after recovering from their first episode. Mean scores on psychopathology measures indicate minimal to low levels of current psychopathology. Comparison of these findings with the existing outcome literature of similar follow- up duration should be made with caution as the majority are of first episode schizophrenia. However our data concerning course type over the most recent two years is consistent with the findings of Mason et al. (1995) and Robinson et al. (2004). However our findings concerning the never psychotic course type over the entire follow- up period differs to that found by Thara et al. (1994). Our study reported a higher percentage (24%) than Thara et al. (1994) (17%) who had not been psychotic during the intervening years and over half of this group had completely remitted. Over half of our cohort was fully occupationally engaged compared with 19% reported by the Scottish Schizophrenia Research Group (1992). The findings from this study suggest patients with psychotic disorders can achieve symptomatic remission and good social and occupational functioning 8-years post FEP