Estimation of general time-varying single particle tracking linear models using local likelihood

In this work, we study a general approach to the estimation of single particle tracking models with time-varying parameters. The main idea is to use local Maximum Likelihood (ML), applying a sliding window over the data and estimating the model parameters in each window. We combine local ML with Expectation Maximization to iteratively find the ML estimate in each window, an approach that is amenable to generalization to nonlinear models. Results using controlled-experimental data generated in our lab show that our proposed algorithm is able to track changes in the parameters as they evolve during a trajectory under real-world experimental conditions, outperforming other algorithms of similar nature.