Spatiotemporal System Identification With Continuous Spatial Maps and Sparse Estimation

Abstract

Abstract-In this paper we present a framework for the identification for spatiotemporal linear dynamical systems. We use a state-space model representation, which has the following attributes: the number of spatial observation locations are decoupled from the model order; the model allows for spatial heterogeneity; the model representation is continuous-over-space; the model parameters can be identified in a simple, sparse estimation procedure. The model identification procedure we propose has four steps: (i) decomposition of the continuous spatial field using a finite set of basis functions. Spatial frequency analysis is used to determine basis function width and spacing such that the main spatial frequency contents of the underlying field can be captured; (ii) initialisation of states in closed form; (iii) initialisation of state-transition and input matrix model parameters using sparse regression -the least absolute shrinkage and selection operator (lasso) method; (iv) joint state and parameter estimation using an iterative Kalman-filter/sparseregression algorithm. To investigate the performance of the proposed algorithm we use data generated by the Kuramoto model of spatiotemporal cortical dynamics. The identification algorithm performs successfully, predicting the spatiotemporal field with high accuracy, whilst the sparse regression leads to a compact model.

A Spatiotemporal Estimation Framework for Real-World LIDAR Wind Speed Measurements

“…where σ φ ∈ R is a parameter defining the basis function width. The basis function width and placement are computed using a spatial frequency analysis technique that follows the work of Sanner and Slotine [31] and applied in a spatiotemporal context in [32]. This approach considers spatial frequency cutoff as the design parameter describing basis function width and placement.…”

“…Since the UKF and most of the state estimation tools do not readily handle nonlinear DAE systems and we cannot treat a descriptor system as a constrained ODE system [14], we make use of a modified UKF algorithm, where the effects of uncertainties and unmodelled dynamics in both difference and algebraic equations may be represented stochastically. In the literature, such uncertainties are typically conveniently represented by zero-mean white Gaussian process noise, such as [5], to account for the effects of assuming 2-D flow and excluding turbine dynamics, and [32], to represent the approximation effects of basis function decomposition. By proceeding similarly for our work, these effects, including those due to time discretisation, are incurred in the forward prediction step.…”

Estimation and Identification of Spatio-Temporal Models with Applications in Engineering, Healthcare and Social Science

“…The weights on the field basis functions and the connectivity kernel form the states and the parameters of the state-space model respectively. The spacing and the width of basis functions can be determined using spatial spectral analysis (Aram et al, 2015b).…”

Hierarchical parameter and state estimation for bilinear systems

“…State and parameter estimation is involved in many applications such as nonlinear systems (Dochain, 2003;Raïssi, Ramdani, & Candau, 2004), stochastic systems (Chen, Morris, & Martin, 2005) and spatiotemporal systems (Aram, Kadirkamanathan, & Anderson, 2015;Dewar & Kadirkamanathan, 2007). A large number of estimation methods such as the Bayesian methods (Krishnanathan, Anderson, Billings, & Kadirkamanathan, 2016;Pan, Yuan, Gonçalves, & Stan, 2016), the maximum likelihood methods (Gu, Liu, Li, Chou, & Ji, 2019), the least squares methods (Mu, Bai, Zheng, & Zhu, 2017), the iterative identification methods (Ding, Xu, Meng, Jin, & Alsaedi, 2019;Pan, Jiang, Wan, & Ding, 2017) and the separated least squares methods (Gan, Chen, Chen, & Chen, 2018;Gan & Li, 2014) have been developed for identification.…”