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

An Estimation Algorithm for General Linear Single Particle Tracking Models with Time-Varying Parameters

“…There are many algorithms for doing localization and linking [43,44] and we assume these steps have been performed prior to applying our approach. Note that while the focus of this paper is model parameter estimation, our algorithm does refine the given trajectories through the filtering and smoothing elements that are integral to our approach; details can be found in, e.g., [26]. The motion in each axis is assumed to be independent and described by a general linear time-varying model in each direction given by…”

“…There are many algorithms for doing localization and linking [ 43 , 44 ] and we assume these steps have been performed prior to applying our approach. Note that while the focus of this paper is model parameter estimation, our algorithm does refine the given trajectories through the filtering and smoothing elements that are integral to our approach; details can be found in, e.g., [ 26 ]. The motion in each axis is assumed to be independent and described by a general linear time-varying model in each direction given by where k is the discrete time index, , , , and are scalars, is the variance of the process noise defined by the diffusion coefficient and the sampling time , and is the variance of the measurement noise as generated by a variety of processes, including shot noise due to the physics of photon generation in fluorescence and read-out noise in the camera.…”

“…However, we found that because the change detection of stage 2 (described below) is not exact, better performance in terms of parameter estimation is achieved by downweighting samples at the edges as they may actually belong to a different model. Note that we have previously established that under this EM scheme, the local likelihood increases at each step and thus this local version inherits the results from standard EM that the algorithm will converge to at least a local maximum [ 26 ].…”

“…As with these prior works, the present paper focuses on systems that discretely jump between different parameter values and builds on our prior efforts using sliding windows and optimal estimation to produce an ML estimate of the parameters [ 25 , 26 ]. Here we describe a novel three stage algorithm that combines change detection to determine when model switches occur with ML estimation to find parameter estimates for each model.…”

Dynamic rEvolution : Adaptive state estimation via Gaussian processes and iterative filtering

“…These requirements necessitate models that are suitable for online updates and computationally efficient algorithms such that updates may be performed at a rate close to the data rate; in control applications, the data rate is often ≥ 100 Hz. It is thus worthwhile to mention that the methods in Section 4.1 are primarily offline methods, even though pragmatic approximations with, e.g., sliding-window optimization exist [134]. The state augmentation approach on the other hand is inherently online, even though it, in general, may not converge to the "true" model, in a system identification sense [15].…”