The instrument-pointing frame (IPF) Kalman filter, and an algorithm that implements this filter, have been devised for calibrating the focal plane of a telescope. As used here, “calibration” signifies, more specifically, a combination of measurements and calculations directed toward ensuring accuracy in aiming the telescope and determining the locations of objects imaged in various arrays of photodetectors in instruments located on the focal plane. The IPF Kalman filter was originally intended for application to a spaceborne infrared astronomical telescope, but can also be applied to other spaceborne and ground-based telescopes.

In the traditional approach to calibration of a telescope, (1) one team of experts concentrates on estimating parameters (e.g., pointing alignments and gyroscope drifts) that are classified as being of primarily an engineering nature, (2) another team of experts concentrates on estimating calibration parameters (e.g., plate scales and optical distortions) that are classified as being primarily of a scientific nature, and (3) the two teams repeatedly exchange data in an iterative process in which each team refines its estimates with the help of the data provided by the other team. This iterative process is inefficient and uneconomical because it is time-consuming and entails the maintenance of two survey teams and the development of computer programs specific to the requirements of each team. Moreover, theoretical analysis reveals that the engineering/science iterative approach is not optimal in that it does not yield the best estimates of focal-plane parameters and, depending on the application, may not even enable convergence toward a set of estimates.

Image In contrast, in the IPF Kalman-filter approach, no attempt is made to distinguish between engineering and scientific parameters. Hence, there is no need for separate engineering and scientific survey teams, separate software, and iteration between the teams. Instead, both engineering and scientific focal-plane parameters are estimated together, using data taken in the same focal-plane survey. The main advantage is that the IPF Kalman filter offers greater efficiency and economy. In addition, the estimates generated by the IPF Kalman filter are optimal.

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 under the Physical Sciences category. NPO-40798

This Brief includes a Technical Support Package (TSP).
Kalman Filter for Calibrating a Telescope Focal Plane

(reference NPO-40798) is currently available for download from the TSP library.

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