Parameter Estimation Using a Modified Version of SPSA Algorithm Applied to State Space Models

Abstract

The objective of this paper is the estimation of unknown static parameters in non-linear non-Gaussian state-space model. The Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm is considered due to its highly efficient gradient approximation. We consider a particle filtering method and employ the SPSA algorithm to maximize recursively the likelihood function. Nevertheless, the SPSA algorithm can become inadequate in models as non-Gaussian state-space model. So that, we have proposed to modify the SPSA algorithm in order to estimate parameters very efficiently in complex models as proposed here reducing its computational cost. An efficient parameter estimator as the Finite Difference Stochastic Approximation (FDSA) algorithm is considered here, in order to compare it with the efficiency of the proposed SPSA algorithm. The proposed algorithm can generate maximum likelihood estimates very efficiently. The performance of proposed SPSA algorithm is shown through simulation using a model with highly multimodal likelihood.