Expectation maximization based framework for joint localization and parameter estimation in single particle tracking from segmented images - Simulation Data

Ratios (SBRs), two different camera types, different diffusion speeds, and two different settings for motion blur. SPT is a class of experimental methods and data analysis techniques for exploring the motion of individual biological macromolecules. Typical estimation algorithms split the problem into two parts: first localize the particle at each data point to generate a trajectory and then estimate model parameters from that trajectory.

We have recently introduced a class of algorithms for jointly estimating both trajectory and model parameters. In this study, we used the data to perform quantitative comparisons between two variants of our approach, one relying on a Sequential Monte Carlo methods combined with Expectation Maximization (SMC-EM) that is applicable to a very broad set of motion and observation models, and one that replaces the SMC elements with methods based on the Unscented Kalman Filter (UKF) to improve upon the computational complexity.

We also compared our methods to two current standards in the field. The first uses Gaussian Fitting to localize the particle, following by a Mean Square Displacement (GF-MSD) analysis to determine model parameters while the other replaces MSD with Maximum Likelihood Estimation (GF-MLE). The main results of our study indicate that our EM-based schemes significantly outperform the existing algorithms at low SBR while at high SBR, GF-MLE performs equally well but at a lower computational cost.