Kalman Filter for Calibrating a Telescope Focal Plane
- Wednesday, 15 November 2006
The IPF Kalman filter is a high-order square-root iterated linearized Kalman filter, which offers robust numerical conditioning and a capability to obtain high accuracy. The filter is parameterized for calibrating the focal plane and aligning the scientific-instrument photodetector arrays with respect to the telescope boresight, all to within a specified tolerance (in the original intended application, a focal-plane radial standard deviation corresponding to 0.14 arc second in the sky). To obtain this level of accuracy, the filter utilizes 37 states to estimate desired alignments while also correcting for systematic errors expected to be caused by optical distortions, the scale factor and misalignment of a scanning mirror, thermomechanically induced drifts of alignments among telescope and instrument frames, and gyroscope bias and bias drift in all axes. Other salient features of the IPF Kalman filter and algorithm include the following:
- The use of polynomial functions of time to characterize such time-dependent behaviors as gyroscope drifts and thermomechanically induced alignment drifts. Because the polynomial coefficients are constant, this feature makes it possible to accommodate such behaviors while retaining the global re-linearization of the Kalman filter.
- A gyroscope-data pre-processing subalgorithm makes it possible to compute and store gyroscope sensitivities in advance, thereby eliminating the need for repeated and time-consuming propagation of gyroscope sensitivities during each filter cycle.
- A parameter-masking capability offers the option of restricting estimation to an arbitrary subset of all the focal-plane parameters, thereby affording flexibility to match calibration mathematical models of different levels of fidelity to different scientific instruments.
- A “multi-run” feature affords flexibility to estimate parameters by use of measurement data, which has been acquired during different observing sessions.
- An experiment design characterized by maneuvers illustrated in the figure provides for observability of all desired parameters and enables the use of the same Kalman filter for a variety of instruments.
- Measurements using observations of both visible and infrared sources can be included in the same set of calibration data.
- There is an option to process centroid information that is partial in the sense that it pertains only to position along a single axis of a photodetector array. Such information is obtained, for example, when calibrating the entrance aperture of spectrometer slit by first scanning a source across the narrow slit width, and then scanning the source along its length.
- The filter algorithm can be executed in one of several optional modes that offer compromises between accuracy and robustness.
This work was done by Bryan Kang and 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 Physical Sciences category. NPO-40798
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