Sequential Monte Carlo Methods for System Identification**This work was supported by the projects Learning of complex dynamical systems (Contract number: 637-2014-466) and Probabilistic modeling of dynamical systems (Contract number: 621-2013-5524), both funded by the Swedish Research Council.

Abstract

One of the key challenges in identifying nonlinear and possibly nonGaussian state space models (SSMs) is the intractability of estimating the system state. Sequential Monte Carlo (SMC) methods, such as the particle filter (introduced more than two decades ago), provide numerical solutions to the nonlinear state estimation problems arising in SSMs. When combined with additional identification techniques, these algorithms provide solid solutions to the nonlinear system identification problem. We describe two general strategies for creating such combinations and discuss why SMC is a natural tool for implementing these strategies. Abstract One of the key challenges in identifying nonlinear and possibly nonGaussian state space models (SSMs) is the intractability of estimating the system state. Sequential Monte Carlo (SMC) methods, such as the particle filter (introduced more than two decades ago), provide numerical solutions to the nonlinear state estimation problems arising in SSMs. When combined with additional identification techniques, these algorithms provide solid solutions to the nonlinear system identification problem. We describe two general strategies for creating such combinations and discuss why SMC is a natural tool for implementing these strategies.

Sequential Ensemble Monte Carlo Sampler for On-Line Bayesian Inference of Time-Varying Parameter in Engineering Applications

“…In this paper, we shall assume that 𝜈 𝜽 follows a zeromean Normal distribution with fixed standard deviation 𝜎 𝜈 (see e.g. [16,18,61]).…”

Identification of stochastic nonlinear models using optimal estimating functions

“…First, the computations of the score function require evaluations of the log-likelihood function and its gradient. Depending on the model, this may be a very challenging task; see [3,35,53]. Second, the performance is sensitive to the distributional assumptions; e.g., the optimal properties of the MLE are only valid if the distribution is correctly specified, otherwise the estimator may even become inconsistent; see for example [68].…”

“…For example, approximate Maximum Likelihood (ML) and Bayesian methods have been developed; see, for example, [29,50,54,69,41,66,64,20,19]. They are mainly based on sequential Monte Carlo (a.k.a particle filters/smoothers) and Markov chain Monte Carlo approximations (see [53]), and have been shown to provide impressive results on several examples and benchmark problems. However, depending on the application, they may be computationally expensive or even infeasible.…”

Recursive identification of a nonlinear state space model

“…The sequential Monte‐Carlo (SMC) methods are well suited for adaptation to grey‐box identification. These algorithms identify nonlinear systems in state space form, based on Bayesian equations 8‐10 . Partly known physical parameters can be included in the dynamic models of some of these Bayesian algorithms, e.g.…”