Robust LPV models identification approach based on shifted asymmetric Laplace distribution

This paper focuses on the robust parameters estimation algorithm of linear parameters varying (LPV) models. The classical robust identification techniques deal with the polluted training data, for example, outliers in white noise. The paper extends this robustness to both symmetric and asymmetric noise with outliers to achieve stronger robustness. Without the assumption of Gaussian white noise pollution, the paper employs asymmetric Laplace distribution to model broader noise, especially the asymmetrically distributed noise, since it is an asymmetric heavy-tailed distribution. Furthermore, the asymmetric Laplace (AL) distribution is represented as the product of Gaussian distribution and exponential distribution to decompose this complex AL distribution. Then, a shifted parameter is introduced as the regression term to connect the probabilistic models of the noise and the predict output that obeys shifted AL distribution. In this way, the posterior probability distribution of the unobserved variables could be deduced and the robust parameters estimation problem is solved in the general Expectation Maximization algorithm framework. To demonstrate the advantage of the proposed algorithm, a numerical simulation example is employed to identify the parameters of LPV models and to illustrate the convergence.