Online Identification of Gaussian-Process State-Space Model with Missing Observations

Abstract

When the state-space model is black-box, it is difficult to identify the system based on the input and observation. In predictive control and other fields, the state and model need to be updated in real time, and online identification becomes very important. However, compared with offline learning, online learning of black-box model is more difficult. This paper proposes an online Bayesian inference and learning method for state-space models with missing observations. When the state-space model is black-box, we expressed it as basis function expansions. Through the connection to the Gaussian processes (GPs), the state and basis function coefficients are updated online. The problems of missing observations caused by the sensor failure are often encountered in practical engineering and are taken into consideration in this paper. In order to keep the online algorithm from being interrupted by missing observations, we update the states and unknown parameters according to whether the observation is missing at the current time. This conservative strategy makes the online learning continuous when the observation is missing, and makes full use of the available statistics in the past. Numerical examples show that the proposed method is robust to missing data and can make full use of the available observations.