Newton-based maximum likelihood estimation in nonlinear state space models**E-mail address to corresponding author: [email protected]. This work is supported by CADICS, a Linnaeus Center, and by the project Probabilistic modeling of dynamical systems (Contract number: 621-2013-5524), both funded by the Swedish Research Council (VR).
Manon Kok, Johan Dahlin, Thomas B. Schön, Adrian Wills · IFAC-PapersOnLine · 2015
Maximum likelihood (ML) estimation using Newton's method in nonlinear state space models (SSMs) is a challenging problem due to the analytical intractability of the loglikelihood and its gradient and Hessian. We estimate the gradient and Hessian using Fisher's identity in combination with a smoothing algorithm. We explore two approximations of the log-likelihood and of the solution of the smoothing problem. The first is a linearization approximation which is computationally cheap, but the accuracy typically varies between models. The second is a sampling approximation which is asymptotically valid for any SSM but is more computationally costly. We demonstrate our approach for ML parameter estimation on simulated data from two different SSMs with encouraging results.