  Single Particle Tracking (SPT) is a powerful class of tools for analyzing the
dynamics of individual biological macromolecules moving inside living cells.
The acquired data is typically in the form of a sequence of camera images that
are then post-processed to reveal details about the motion. In this work, we
develop an algorithm for jointly estimating both particle trajectory and motion
model parameters from the data. Our approach uses Expectation Maximization (EM)
combined with an Unscented Kalman filter (UKF) and an Unscented
Rauch-Tung-Striebel smoother (URTSS), allowing us to use an accurate, nonlinear
model of the observations acquired by the camera. Due to the shot noise
characteristics of the photon generation process, this model uses a Poisson
distribution to capture the measurement noise inherent in imaging. In order to
apply a UKF, we first must transform the measurements into a model with
additive Gaussian noise. We consider two approaches, one based on variance
stabilizing transformations (where we compare the Anscombe and Freeman-Tukey
transforms) and one on a Gaussian approximation to the Poisson distribution.
Through simulations, we demonstrate efficacy of the approach and explore the
differences among these measurement transformations.
