  Viscoelastic material properties at high strain rates are needed to model
many biological and medical systems. Bubble cavitation can induce such strain
rates, and the resulting bubble dynamics are sensitive to the material
properties. Thus, in principle, these properties can be inferred via
measurements of the bubble dynamics. Estrada et al. (2018) demonstrated such
bubble-dynamic high-strain-rate rheometry by using least-squares shooting to
minimize the difference between simulated and experimental bubble radius
histories. We generalize their technique to account for additional
uncertainties in the model, initial conditions, and material properties needed
to uniquely simulate the bubble dynamics. Ensemble-based data assimilation
minimizes the computational expense associated with the bubble cavitation
model. We test an ensemble Kalman filter (EnKF), an iterative ensemble Kalman
smoother (IEnKS), and a hybrid ensemble-based 4D--Var method (En4D--Var) on
synthetic data, assessing their estimations of the viscosity and shear modulus
of a Kelvin--Voigt material. Results show that En4D--Var and IEnKS provide
better moduli estimates than EnKF. Applying these methods to the experimental
data of Estrada et al. (2018) yields similar material property estimates to
those they obtained, but provides additional information about uncertainties.
In particular, the En4D--Var yields lower viscosity estimates for some
experiments, and the dynamic estimators reveal a potential mechanism that is
unaccounted for in the model, whereby the viscosity is reduced in some cases
due to material damage occurring at bubble collapse.
