Abstract
<title>Abstract</title> <p>This study presents complementary approaches to mitigate the impact of random measurement noise on velocity and acceleration statistics obtained from Lagrangian Particle Tracking (LPT). Using synthetically generated particle tracks in a turbulent near-wall channel flow, we assess both track-level processing and statistical noise separation strategies. First, an adaptive extension of the conventional TrackFit algorithm is introduced, in which filter parameters are adjusted to local flow conditions rather than prescribed globally. This local TrackFit approach enables accurate estimation of instantaneous velocities and, in particular, accelerations, even in strongly inhomogeneous regions such as the viscous sublayer, where conventional global filtering leads to significant bias. Furthermore, this extension of the TrackFit concept enables more accurate prediction of particle positions, as required in Shake-The-Box (STB) algorithms. Second, track-merging strategies are assessed to combine statistically independent track segments of the same particle obtained from multiple temporally shifted tracking passes, thereby enhancing accuracy in variable-timestep LPT. Third, a statistical noise correction framework based on Gaussian error propagation is introduced, in which measurement noise is explicitly separated from the second-order moment estimates of velocity and acceleration. This approach does not rely on strong temporal filtering and therefore avoids underestimation of the corresponding moments. Together, these methods enable accurate estimation of instantaneous Lagrangian velocities and accelerations through adaptive track filtering, while allowing noise-robust velocity and acceleration statistics to be obtained without filtering via explicit noise subtraction.</p>