Estimation of lumped cerebral arterial radius is important for healthcare monitoring in ICU patients, specially for detecting the presence of vasospasm following Subarachnoid Hemorrhage. A technique for continuous monitoring based on available measurements without introducing any additional invasive technique is very attractive, and would allow detection of vasospasm earlier and more accurately than other methods such as angiography. Our proposed estimation approach uses a combination of parameter estimation and state estimation techniques, and relies heavily on mathematical models of cerebral hemodynamics.We presented two models based on previous work by Ursino et. al, and showed through simulation how a simpler Model 2, with only four state-variables could predict changes in arterial radius from the signals generated through Model 1. We showed how to estimate the parameters of Model 1 through a non-linear least-squares technique, and how we trained the model on the first available recording of every patient. Then we applied our state-estimation approach using DD1 filtering, and a DD1 filter with constraints (QCKF). We showed that our approach detected the presence of vasospasm for Patient A, and observed a radius evolution that matches the expected results. The QCKF produced smaller errors in the output estimation, indicating that constraining the states to be within reasonable limits may improve the accuracy of the estimation. We also estimated the arterial radius for Patient B, which had a constant mild vasospasm throughout the recordings. In essence, we have shown the potential of Kalman-like state-estimators for nonlinear models. This application could potentially save lives by predicting post-SAH vasospasm before other techniques would.