A new method of calculating the root-mean-square (rms) pointing jitter of a scientific instrument (e.g., a camera, radar antenna, or telescope) is introduced based on a state-space concept. In comparison with the prior method of calculating the rms pointing jitter, the present method involves significantly less computation.

The rms pointing jitter of an instrument (the square root of the jitter variance shown in the figure) is an important physical quantity which impacts the design of the instrument, its actuators, controls, sensory components, and sensor-output-sampling circuitry. Using the Sirlin, San Martin, and Lucke definition of pointing jitter, the prior method of computing the rms pointing jitter involves a frequency-domain integral of a rational polynomial multiplied by a transcendental weighting function, necessitating the use of numerical-integration techniques. In practice, numerical integration complicates the problem of calculating the rms pointing error. In contrast, the state-space method provides exact analytic expressions that can be evaluated without numerical integration.

Instantaneous and Statistical Quantities are used to characterize the pointing of an instrument (that is, rotation of the instrument about an axis). The quantities shown here pertain to a pointing process y(t) at instant of time t during an observation interval (window) of duration T that starts at time t, E[] is an expectation operator denoting the ensemble average of the bracketed term, n(t) is a zero-mean white-noise process, and Cov[] is an ensemble-average covariance operator.
The theoretical foundation of the state-space method includes a representation of the pointing process as a stationary process generated by a state-space model driven by white noise. The state-space formulation results in the replacement of the aforementioned weighted frequency integral with the calculation of a matrix exponential. Additional simplifications may be possible in certain applications by taking advantage of well-known matrix exponential expressions and/or inverse Laplace transform relationships. Two useful examples of such simplifications are given in the report. In addition to simplifying the calculations, the closed-form expressions provide insight into physical mechanisms of jitter.

This work was done by David Bayard of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com/tsp under the Information Sciences category. NPO-30525.

Topics:
Analysis methodologies Antennas Data management Electronic equipment Exteriors Imaging and visualization Information Technology Noise Optics Radar Sensors and actuators Statistical analysis Telescopes Terminology Windows and windshields
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Analytic Method for Computing Instrument Pointing Jitter

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NASA Tech Briefs Magazine

This article first appeared in the January, 2003 issue of NASA Tech Briefs Magazine (Vol. 27 No. 1).

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Overview

The document presents a technical report on an innovative analytic method for computing instrument pointing jitter, specifically aimed at improving the performance of spacecraft pointing systems. Authored by David S. Bayard and prepared under the auspices of the Jet Propulsion Laboratory (JPL) for NASA, the report outlines a new state-space approach that allows for the evaluation of root-mean-square (RMS) pointing jitter without the need for numerical integration.

Traditionally, the evaluation of RMS pointing jitter has relied on complex frequency domain integrals involving rational polynomials and transcendental weighting functions. This reliance on numerical methods has posed significant challenges, making the calculations computationally expensive and inconvenient for practical engineering applications. The new method introduced in this report overcomes these limitations by providing a state-space representation that is applicable to a wide range of pointing processes, particularly stationary processes with arbitrary rational spectra.

The report emphasizes the importance of accurately characterizing spacecraft pointing systems, as this is crucial for defining requirements, designing controllers and estimators, selecting sampling times, and sizing actuators and sensors. The proposed state-space method not only simplifies the evaluation process but also enhances the usability of jitter analysis in common engineering tools, such as spreadsheets.

In addition to detailing the novel approach, the document acknowledges the contributions of Dr. Sam Sirlin from JPL for his technical discussions and insights. It also references previous works that utilized numerical integration for jitter evaluation, highlighting the advantages of the new method over these traditional approaches.

The report concludes with a notice regarding the sponsorship of the research by NASA and clarifies that the use of any specific commercial products or services mentioned does not imply endorsement by the U.S. Government or JPL.

Overall, this document represents a significant advancement in the field of spacecraft pointing control, offering a more efficient and practical solution for engineers and researchers involved in the design and analysis of scientific instruments.