Directional Pareto optimized Kalman filtering with Demyanov–Rubinov subdifferentials for robust pollution concentration prediction

Abstract

The study introduces a novel framework that enhances Kalman filtering for the prediction of environmental pollution by integrating Pareto optimization with Demyanov–Rubinov (DR) subdifferential theory and highlights the potential of integrating non-smooth variational tools into classic state estimation frameworks. The proposed method addresses the challenges posed by abrupt fluctuations, measurement noise, and non-smooth system dynamics typically found in real-world environmental monitoring. Our approach simultaneously optimizes two key objectives: prediction accuracy and computational efficiency. By modeling these as direction-sensitive objectives and embedding them in a multi-objective optimization routine, we enable the Kalman filter to dynamically adapt its gain selection based on system behavior. Unlike traditional Kalman filters, which assume smooth system characteristics, our DR-enhanced formulation employs upper directional derivatives, based on DR subdifferentials, to handle non-convex and non-smooth variations in pollutant signals, which allows the filter to respond more effectively to sudden environmental changes and sensor delays, especially in systems with inertial components like biofilters. Through the use of sublinear and superlinear approximations, the filter gain is adjusted adaptively along the most informative directions of uncertainty. The methodology is validated in a laboratory biofiltration setup, where it is compared with particle filtering and NARX neural networks in rule-based forecasting strategies. Experimental results demonstrate that our method achieves superior adaptability and robustness, improving prediction accuracy by up to 88% and significantly reducing system response lag.