Nonparametric multi-step prediction in nonlinear state space dynamic systems

A Nonparametric Multi-step Prediction Estimator in Markovian Structures

In this paper, a multistage kernel smoother is proposed to estimate the conditional mean E(Z | X) in a Markovian structure where the observations (Xi, Yi, Zi) are i.i.d. samples from a distribution that possesses the Markov property E(Z | Y, X) = E(Z | Y ). We prove that the asymptotic mean squared error of the proposed estimator is smaller than that using the Nadaraya-Watson estimator directly...

Bayesian Inference in Nonparametric Dynamic State-Space Models

We introduce state-space models where the functionals of the observational and the evolutionary equations are unknown, and treated as random functions evolving with time. Thus, our model is nonparametric and generalizes the traditional parametric state-space models. This random function approach also frees us from the restrictive assumption that the functional forms, although time-dependent, ar...

Nonparametric Bayesian state estimation in nonlinear dynamic systems with a-stable measurement noise

In signal processing literature, noise’s source are often assumed to be Gaussian. However, in many fields the conventional Gaussian assumption is inadequate and leads to the loss of accuracy and/or resolution. This is particularly the case of applications operating at high frequency (60GHz) such as the internet of objects. In such context, underlying signals exhibit impulsive nature and do not ...

Nonparametric output prediction for nonlinear fading memory systems

The authors construct a class of elementary nonparametric output predictors of an unknown discrete-time nonlinear fading memory system. Their algorithms predict asymptotically well for every bounded input sequence, every disturbance sequence in certain classes, and every linear or nonlinear system that is continuous and asymptotically time-invariant, causal, and with fading memory. The predicto...

Identification of nonlinear systems using Polynomial Nonlinear State Space models