The Gain-Scheduled Filter With Probability Density Function Compensator for Stochastic System With Missing Measurements and Gaussian Mixture Noise

A hybrid filtering strategy, including the gain-scheduled filter (GSF) and probability density function (PDF) compensation, is proposed for a discrete system with missing measurements and Gaussian mixture noise. Commonly, the estimate error is strictly controlled to 0 is impossible in a complex environment. The aim of the proposed filter is to stabilize the filtering dynamics in the mean square sense and to ensure the estimate error PDF close to the desired PDF as much as possible. The GSF is designed via appropriate linear matrix inequalities (LMIs), and the PDF compensator is proposed based on the real-time Wasserstein distance between the past data and the desired distribution to force the estimate error distribution to track the desired distribution. Two comparison experiments are performed to verify the effectiveness of the proposed method.