## 3 Results
### Example Task and Physiological Measurement  
One of the major requirements in designing a clinical movement control test for detecting PPD is that the test should be simple and easy to execute. There are various possible clinical movement control tests, such as a spiral tracing task, in which the subject needs to trace a spiral drawn on white paper [63]; an eye tracking task, in which the subject needs to follow a circle displayed on a screen [64; 65]; a compensatory tracking task, in which the subject needs to maintain the actual position of the arm with a zero reference (or initial) position of an arm displayed on the screen in the presence of an outside influence by means of compensating for the error in arm position [66]. In this work, we consider pupil dilation/constriction data to apply the proposed method. A significant latency is  
Figure 5: Box plot of a synthetic data set (total 1000 individuals, 500 individuals in each group) of the real part of estimated poles for 9 time units (each unit may represent several months) for simulated healthy and simulated PPD for (**a**) a gradual increment in delay and (**b**) gradual increment in gain. It is observed that the real part of the estimated poles remains in the same range for simulated healthy individuals and increases for simulated PPD over a significant period of time. reported during the pupillary light reflex in patients with Parkinson's disease [67, 68], and this latency increases with the progression of the disease [69]. This latency degrades the stability of the sensory-motor loop representing the pupillary-light-reflex. Therefore, the proposed method is applicable in this situation. It is worth noting that the proposed method is equally applicable to any of the other motor control tasks mentioned above. We developed a pupilometer in the lab, as shown in Figure 6a, that uses a camera, infrared light sources, and LEDs to stimulate the pupil (with light flashes). With this pupilometer and its onboard microcontroller, it is possible to produce different stimulation patterns of white LEDs switching on and off, and the resulting pupil response is recorded as a video. Further, using relatively straightforward image processing techniques, the pupil diameter as a function of time is estimated from the recorded video. This is a simple portable device and a comfortable task for patients and can be conducted in any clinical environment without any special arrangements. A sample screenshot of the video recorded by the device after applying image processing to detect the pupil diameter is shown in Figure 6b. The device was utilized to gather data from both age-matched healthy control subjects and patients with Parkinson's disease (PD). Prior to participating in the experiment, all participants provided written informed consent, and the institute's ethics committee approved the experimental protocols. During the test, participants were instructed to focus on the red LED located at the center of the screen, with the LED light source being turned on for 10 s and then turned off for 10 s. The procedure was repeated five times within a single trial, and three sets of trials were conducted. The pupil diameter data obtained from each trial was considered a step response, and matrix pencil methods were employed to estimate poles representing the motor control dynamics. The output of the pupil detection algorithm for a few representative PD patients (6) and age-matched healthy individuals (6) are shown in Figure 7. A total of 63 trials were conducted, and MPM was used to detect poles for all these trials; the pole data are not reported here, as the absolute values are irrelevant, and only long-term trends are relevant. The data show the feasibility of setting up a simple clinical task and the ability to generate good quality data that the MPM is able to process to generate estimates of poles. The machine-learning-based classification algorithm is, however, not applied here, as that will require long-term data from a longitudinal study.