SUMMARYThe presence of outliers can considerably degrade the performance of linear recursive algorithms based on the assumptions that measurements have a Gaussian distribution. Namely, in measurements there are rare, inconsistent observations with the largest part of population of observations (outliers). Therefore, synthesis of robust algorithms is of primary interest. The Masreliez-Martin filter is used as a natural frame for realization of the state estimation algorithm of linear systems. Improvement of performances and practical values of the Masreliez-Martin filter as well as the tendency to expand its application to nonlinear systems represent motives to design the modified extended Masreliez-Martin filter. The behaviour of the new approach to nonlinear filtering, in the case when measurements have non-Gaussian distributions, is illustrated by intensive simulations.

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Joint estimation of states and time-varying parameters of linear stochastic systems is of practical importance for fault diagnosis and fault tolerant control. The known fact is that measurements have outliers. They can significantly degrade the properties of linearly recursive algorithms, which are designed to work in presence of Gaussian noises. This article proposes two kinds of strategies for joint parameter-state robust estimation of linear stochastic models in presence of all possible faults and non-Gaussian noises. In the form of Theorem, joint robust algorithm for systems with sensor and component faults, as well as the algorithm for systems with parameter faults are proposed. Because of their good features in robust filtering, Masreliez-Martin filter represents a cornerstone for realization of the proposed robust algorithms for joint state-parameter estimation. The good features of proposed robust estimation algorithms, in relation to algorithms based on other widely-used filters, are illustrated by simulation results. On the other side, intensive research in the field of mathematical modeling of pneumatic servo drives has shown that their mathematical models are nonlinear in which a lot of important details cannot be included in the model. Also, it has been well known that the nonlinear model can be approximated by a linear model with time-varying parameters. Due to the abovementioned reasons, it can be assumed that the pneumatic cylinder model is a linear stochastic model with variable parameters. The good practical values of the proposed robust joint algorithm to identification of the pneumatic cylinder are illustrated by experimental results.