  A turbulent boundary layer is an essential flow case of fundamental and
applied fluid mechanics. However, accurate measurements of turbulent boundary
layer parameters (e.g., friction velocity $u_\tau$ and wall shear $\tau_w$),
are challenging, especially for high speed flows (Smits et al., 2011). Many
direct and/or indirect diagnostic techniques have been developed to measure
wall shear stress (Vinuesa et al., 2017). However, based on different
principles, these techniques usually give different results with different
uncertainties. The current study introduces a nonlinear data assimilation
framework based on the Unscented Kalman Filter that can fuse information from
i) noisy and gappy measurements from Stereo Particle Image Velocimetry, a
Preston tube, and a MEMS shear stress sensor, as well as ii) the uncertainties
of the measurements to estimate the parameters of a turbulent boundary layer. A
direct numerical simulation of a fully developed turbulent boundary layer flow
at Mach 0.3 is used first to validate the data assimilation algorithm. The
algorithm is then applied to experimental data of a flow at Mach 0.3, which are
obtained in a blowdown wind tunnel facility. The UKF-based data assimilation
algorithm is robust to uncertain and gappy experimental data and is able to
provide accurate estimates of turbulent boundary layer parameters.
