Abstract
This paper is concerned with the problem of recursive system identification using nonparametric Gaussian process model. Non-linear stochastic system in consideration is affine in control and given in the input-output form. The use of recursive Gaussian process algorithm for non-linear system identification is proposed to alleviate the computational burden of full Gaussian process. The problem of an online hyper-parameter estimation is handled using proposed ad-hoc procedure. The approach to system identification using recursive Gaussian process is compared with full Gaussian process in terms of model error and uncertainty as well as computational demands. Using Monte Carlo simulations it is shown, that the use of recursive Gaussian process with an ad-hoc learning procedure offers converging estimates of hyper-parameters and constant computational demands.
Highlights
Throughout the sciences the task of building models from observed data is of fundamental importance
We propose the use of Recursive Gaussian Process (RGP) regression algorithm for system identification task, which is described
The RGP algorithm was compared with the full GP (FGP) approach in terms of computational demands per iteration as well as the Root mean square error (RMSE) and the logarithm of average predictive variance
Summary
Throughout the sciences the task of building models from observed data is of fundamental importance. In situations, where the real-time data processing is required, the size of the matrix k(X, X) grows, which leads to ever increasing computational demands for matrix inversion in each time step as more and more data are being processed To alleviate this problem, we propose the use of RGP regression algorithm for system identification task, which is described . 3. Recursive Gaussian process regression This section covers the identification of a non-linear stochastic system by means of the RGP regression algorithm. The idea of the proposed ad-hoc approach lies in the treatment of the current estimate of the latent function values μgk as perfect observations In practical terms this entails modification of the marginal likelihood objective function (17), whereby the noisy observations Yk are replaced with the perfect observations μgk at basis vector locations X. The notation Kθ emphasizes the fact that the prior covariance matrix is a function of hyper-parameters θ
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