Graph-Frequency Domain Kalman Filtering for Industrial Pipe Networks Subject to Measurement Outliers

This article is concerned with the outlier-resistant state estimation problem for industrial pipe networks (PNs). PN signals, e.g., pressure and temperature, are modeled as low-pass time-varying graph signals, and an outlier-resistant graph-frequency domain (GFD) filter is proposed. This article extends the innovation saturation (IS) mechanism from the node domain to the GFD. A GFD IS function is developed with a more compact structure, which reduces outlier effects by restricting PN signals' smoothness. Since the PN signal is time-varying, the saturation function is embedded in the Kalman filter as an inequality constraint. The close-form solution to the filter is derived by replacing the nonlinear inequality constraints with high-pass graph Fourier transforms, and the cutoff frequency is found by analyzing the graph-frequency component of prior and posterior. A steel industrial PN is used to evaluate the proposal. Results indicate that the proposed filter exhibits superior performance in PN systems, particularly internal nodes.