Study On Online Algorithm Based On Gaussian Process Regression And Its Application

Gaussian Process Regression(GPR)is a Bayesian machine learning method with adaptability and empirical learning capability.This paper focuses on the GPR model with explicit mathematical explanations and good prediction ability,and conducts a relatively systematic study of the batch training and online methods of GPR.Two new online GPR algorithms are proposed:a sparse online method based on inducing points and an iterative algorithm based on spherical square root unscented Kalman filtering.These algorithms are successfully applied to channel blind equalization problems.The main contributions of this paper are as follows.(1)In response to the problem of continuously increasing computational complexity of GPR in online scenarios,a sparse method based on inducing points is proposed to reduce the computational complexity.This method reduces the computational demand of the model by selecting and using inducing points instead of large training data.To further improve computational efficiency,block matrix inversion theory is used to limit the dimension of the covariance matrix,ensuring the model’s memory and time occupancy.Experimental results show that this method significantly improves computation speed while ensuring prediction accuracy.(2)A method is proposed to combine spherical square root unscented Kalman filtering with Gaussian process regression to handle online input data.In the proposed model,the hyperparameters are treated as states,and it is assumed that the hyperparameters do not change after the model converges.Therefore,the state of the unscented Kalman filter is a translation state,and the model’s prediction equation is nonlinearly mapped through Gaussian process regression.After repeated iterations of the state equation and prediction equation,the model can predict the input data.(3)Based on the online Gaussian process regression algorithm proposed in this paper,which is based on the sparse method,the application effect of this algorithm in channel blind equalization is studied.Experimental results show that this algorithm has good prediction accuracy and computational speed,which is superior to other online blind equalization methods.