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# Analytic Method for Computing Instrument Pointing Jitter

- Wednesday, 24 January 2007

### Jitter can be computed more efficiently.

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.

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.*

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