A Pointing Covariance Analysis Tool (PCAT) has been developed for evaluating the expected performance of the pointing control system for NASA’s Space Interferometry Mission (SIM). The SIM pointing control system is very complex, consisting of multiple feedback and feedforward loops, and operating with multiple latencies and data rates. The SIM pointing problem is particularly challenging due to the effects of thermomechanical drifts in concert with the long camera exposures needed to image dim stars.
Other pointing error sources include sensor noises, mechanical vibrations, and errors in the feedforward signals. PCAT models the effects of finite camera exposures and all other error sources using linear system elements. This allows the pointing analysis to be performed using linear covariance analysis. PCAT propagates the error covariance using a Lyapunov equation associated with time-varying discrete and continuous-time system matrices. Unlike Monte Carlo analysis, which could involve thousands of computational runs for a single assessment, the PCAT analysis performs the same assessment in a single run. This capability facilitates the analysis of parametric studies, design trades, and “what-if” scenarios for quickly evaluating and optimizing the control system architecture and design.
This work was done by David Bayard and Bryan Kang of Caltech for NASA’s Jet Propulsion Laboratory.
NPO-45308
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Using Covariance Analysis To Assess Pointing Performance
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Overview
The document discusses the development and application of a new mathematical analysis method, specifically covariance analysis, to assess pointing performance for NASA's Space Interferometer Mission (SIM). The SIM project aims to detect and characterize Earth-like planetary systems around neighboring stars using interferometric-based astrometry. A critical challenge in this mission is the accurate tracking of dim stars, which is complicated by long camera exposure times and the limitations of feedback control systems.
To address these challenges, the SIM Pointing Covariance Analysis Tool (PCAT) was developed. This tool models the complex feedback and feed forward control architecture of the SIM pointing system, which includes both digital and analog components. The analysis incorporates a generalized Lyapunov equation with time-varying system matrices to propagate error covariance, effectively capturing the multi-rate and multi-loop nature of the pointing system.
The document highlights the fundamental trade-offs involved in dim-star pointing, particularly the balance between thermal drift noise, which worsens with longer exposures, and measurement noise from camera centroiding errors, which improves with longer exposures. The analysis identifies optimal exposure times based on star magnitude and type, leading to a family of optimal designs that outline the best attainable RMS pointing performance.
PCAT is specialized for two main applications: PCAT-S for science pointing performance and PCAT-G for guide pointing performance. The results indicate that SIM's guide pointing control and angle feed forward accuracy requirements can be met using a 10 Hertz controller with a 5 Hertz angle feed forward cutoff filter. The document also discusses the impact of latency on control design and provides recommendations for future efforts.
One of the key advantages of covariance analysis over traditional Monte Carlo methods is its ability to calculate RMS pointing performance in a single run, allowing for fast turnaround performance predictions and efficient evaluation of various design scenarios. This capability is particularly beneficial for the SIM project, where performance evaluation across multiple parameters—such as star types, magnitudes, and exposure times—is essential.
Overall, the document emphasizes the innovative approach taken by NASA to enhance pointing performance in complex astronomical observations, showcasing the significance of covariance analysis in aerospace technology.
