<div>Process optimization and control can become challenging when the measurements are affected by irregular noise. Classical approaches utilize Gaussian method like Kalman filtering to alleviate the sensory noise. However, many industries involve skewed noise in their processes. While the closed skew normal (CSN) distribution generalizes a Gaussian distribution with additional parameters, its dimension increases during recursive estimation, making it impractical. Even though there exist some techniques for the solution, they are typically either too complicated or inaccurate for the higher dimensional problems. This study proposes a novel online optimization scheme to reduce the dimensionality of a CSN distribution while considering the properties of the complete empirical distribution. Since the objective function used during the optimization step considers the geometry of the metric space, the proposed scheme achieves the higher accuracy without sacrificing computational efficiency. After finding the reliable combination of objective function and optimizer, the proposed filter is applied to two real-time pilot-scale experiments. The results indicate that it is beneficial for recursive state estimation in the presence of skewed noise.<br></div>

<div>Process optimization and control can become challenging when the measurements are affected by irregular noise. Classical approaches utilize Gaussian method like Kalman filtering to alleviate the sensory noise. However, many industries involve skewed noise in their processes. While the closed skew normal (CSN) distribution generalizes a Gaussian distribution with additional parameters, its dimension increases during recursive estimation, making it impractical. Even though there exist some techniques for the solution, they are typically either too complicated or inaccurate for the higher dimensional problems. This study proposes a novel online optimization scheme to reduce the dimensionality of a CSN distribution while considering the properties of the complete empirical distribution. Since the objective function used during the optimization step considers the geometry of the metric space, the proposed scheme achieves the higher accuracy without sacrificing computational efficiency. After finding the reliable combination of objective function and optimizer, the proposed filter is applied to two real-time pilot-scale experiments. The results indicate that it is beneficial for recursive state estimation in the presence of skewed noise.<br></div>