Tumor-tracking in radiotherapy: parameterization of sensor time-delay compensators and associated performance limitations

Motivated by research into tumour tracking in radiotherapy, this paper considers the problem of constructing a linear time-invariant asymptotic estimator to predict the tumour location in real time. The challenge in the estimator design is to accommodate a time delay associated with the sensor, which in this case is an X-ray imager and associated image processor. The contributions of this paper are first, to show that the class of estimators which achieves perfect asymptotic estimation can be parameterized in a manner similar to the well-known Youla parameterization of stabilizing feedback controllers, and, second, to prove that there are fundamental limits on the performance levels that can be achieved. Aspects of performance considered include disturbance rejection, sensor noise rejection, and sensitivity to model uncertainty. The results are restricted to single-input single-output discrete-time linear time-invariant systems