Trevor T. Ashley

Method for simultaneous localization and parameter estimation in particle tracking experiments

We present a numerical method for the simultaneous localization and parameter estimation of a fluorescent particle undergoing a discrete-time continuous-state Markov process. In particular, implementation of the method proposed in this work yields an approximation to the posterior density of the particle positions over time in addition to maximum likelihood estimates of fixed, unknown parameters. The method employs sequential Monte Carlo methods and can take into account complex, potentially nonlinear noise models, including shot noise and camera-specific readout noise, as well as a wide variety of motion models and observation models, including those representing recent engineered point spread functions. We demonstrate the technique by applying it to four scenarios, including a particle undergoing free, confined, and tethered diffusions.

A Sequential Monte Carlo framework for the system identification of jump Markov state space models

We propose a Maximum Likelihood-based method that combines the Expectation Maximization algorithm with Sequential Monte Carlo methods to estimate fixed parameters and transition probabilities for a general class of nonlinear jump Markov systems in state space form. This method is an extension to a previous method originally proposed by T. B. Schön, A. Wills, and B. Ninness for identifying the parameters of a class of nonlinear systems that are not dependent on a Markov chain. In this work, we detail an extension of this method to jump Markov systems and illustrate it through its application to identifying the parameters of the logistic map driven by white Gaussian noise with variance governed by a discrete Markov process.

Validation of a nonlinear reactive control law for three-dimensional particle tracking in confocal microscopy

A nonlinear control law for reactively tracking a diffusing fluorescent particle in three dimensions is reviewed and preliminary experimental results are presented. The control law, originally derived in the context of exploring scalar potential fields, converges to a volume around the maximum of the point spread function of a confocal microscope using very little information of the underlying structure of the field. Experimental results show the control law can track particles with diffusion coefficients over 3 μm2/s with moderate excitation intensities.

A control law for seeking an extremum of a three-dimensional scalar potential field

We describe an extension to a two-dimensional extremum seeking control law so that it may seek an extremum of a three-dimensional scalar potential field. We derive an equilibrium trajectory and prove its local stability for the case of a parabolic potential field. We then numerically characterize the stability as a function of parameters by evaluating its Floquet multipliers.