Lightweight Approach for Nonlinear State-Space System Identification Subjected to Skewed Measurement Noise

In this paper, the skewed output noise is considered and we propose a lightweight robust algorithm for nonlinear state-space system identification based on the generalized hyperbolic variance gamma (GHVG) distribution, which enhances the robustness of the proposed algorithm. To facilitate the realization of the proposed algorithm, the hidden variables are introduced to decompose the GHVG distribution into the Gaussian gamma mixture (GGM) distribution, which improves the computational efficiency of the proposed algorithm. The expectation maximization (EM) and the particle smoothing (PS) approaches are combined to solve the hidden variables and unknown states problems, which contributes to derive the estimation formulas of the model parameters and noise parameters simultaneously. To further reduce the computational burden of PS method for estimating the nonlinear states, a novel nearest neighbor idea is used in the identification process which ensures the performance of the proposed algorithm while reducing the number of particles involved in the calculation of the cost function. Finally, the verification results are fairly carried out to demonstrate the effectiveness of the proposed algorithm. Note to Practitioners—The nonlinear state-space model (NSSM) is widely applied in industrial processes due to its ability to characterize the internal dynamics of the system. For probability-based identification of NSSM, the Gaussian or heavy-tailed distributions with symmetric statistical properties are commonly used, which may limit their application in practical industrial settings. Motivated by this problem, this paper proposes a lightweight robust identification algorithm of NSSM based on GHVG distribution. An improved PS method based on nearest neighbor idea is also introduced to reduce the computational efficiency of the algorithm while ensuring its performance. This means that the proposed method is not only robust to the outliers and the skewed output noise, but also greatly reduces the running time of the algorithm, which can extend its application in real industrial processes.