Algorithm for the identification of malfunctioning sensors in the control systems of segmented mirror telescopes

The active control systems of segmented mirror telescopes are vulnerable to a malfunction of a few (or even one) of their segment edge sensors, the effects of which can propagate through the entire system and seriously compromise the overall telescope image quality. Since there are thousands of such sensors in the extremely large telescopes now under development, it is essential to develop fast and efficient algorithms that can identify bad sensors so that they can be removed from the control loop. Such algorithms are nontrivial; for example, a simple residual-to-the-fit test will often fail to identify a bad sensor. We propose an algorithm that can reliably identify a single bad sensor and we extend it to the more difficult case of multiple bad sensors. Somewhat surprisingly, the identification of a fixed number of bad sensors does not necessarily become more difficult as the telescope becomes larger and the number of sensors in the control system increases.