Godoy Boris I, Lin Ye, Andersson Sean B
Department of Mechanical Engineering, Boston University, Boston, MA 02215, USA.
Division of Systems Engineering, Boston University, Boston, MA 02215, USA.
Proc Am Control Conf. 2020 Jul;2020:5151-5156. doi: 10.23919/acc45564.2020.9147877. Epub 2020 Jul 27.
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 a local time-varying estimation algorithm for estimating motion model parameters from the data considering nonlinear observations. Our approach uses several well-known existing tools, namely the Expectation Maximization (EM) algorithm combined with an Unscented Kalman filter (UKF) and an Unscented Rauch-Tung-Striebel smoother (URTSS), and applies them to the time-varying case through a sliding window methodology. 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 our time-varying approach to the UKF, we first need to transform the measurements into a model with additive Gaussian noise. This is carried out using a variance stabilizing transform. Results from simulations show that our approach is successful in tracing time-varying diffusion constants at a range of physically relevant signal levels. We also discuss the initialization for the EM algorithm based on the available data.
单粒子追踪（SPT）是一类强大的工具，用于分析活细胞内单个生物大分子的动力学。获取的数据通常是一系列相机图像的形式，然后对其进行后处理以揭示运动细节。在这项工作中，我们开发了一种局部时变估计算法，用于从考虑非线性观测的数据中估计运动模型参数。我们的方法使用了几种现有的知名工具，即期望最大化（EM）算法与无迹卡尔曼滤波器（UKF）和无迹Rauch-Tung-Striebel平滑器（URTSS）相结合，并通过滑动窗口方法将它们应用于时变情况。由于光子产生过程的散粒噪声特性，该模型使用泊松分布来捕获成像中固有的测量噪声。为了将我们的时变方法应用于UKF，我们首先需要将测量值转换为具有加性高斯噪声的模型。这是使用方差稳定变换来实现的。模拟结果表明，我们的方法成功地在一系列物理相关信号水平上追踪时变扩散常数。我们还讨论了基于可用数据的EM算法初始化。
