The State Vector Optimal Estimates for Discrete Stochastic Systems With Uncertain Perturbations and Noise

Abstract

Assessment of the dynamic systems state is widely used in various areas of technical activity. In practice, the most well-known and common methods of estimation are the methods of the Kalman filter and Luenberger observers. Most of the results known in the scientific literature for constructing estimates of the dynamic systems state in the presence of acting uncontrolled disturbances and noise are associated with stationary systems. The insensitivity of such estimates to the influence of accompanying uncontrolled perturbations is ensured by the introduction of certain restrictions that are imposed on a number of system matrices, and their optimality is achieved by minimizing the estimation errors covariance matrix trace due to those degrees of freedom that remained after the separation procedure was performed. The aim of the work is to develop a filter capable of generating state vector optimal estimates of a stochastic linear system with changeable parameters that are insensitive to the influence of uncontrolled inputs. In this case, the conditions that guarantee the convergence of the estimates obtained must be easily verifiable. The goal is achieved by using a one-to-one transformation of the equations of systems, followed by the application of the Kalman filter. The O'Reilly functional observer is used as the specified transformation. An example is given that illustrates the effectiveness of the proposed filter.