Square-root filtering method for continuous identification of industrial systems

The article deals with the possibility of using the square-root filtering methods to guarantee numerical stability of continuous identification during long-term monitoring of time-varying industrial systems. The main emphasis is being placed on long-term deployment, therefore the process of recursive computation of the covariance matrix $P_{(k)}$ in the form of regression analysis is discussed in detail. The application of regression analysis in form of a generalized least-squares method for the purpose of weighting a posteriori information is solved by using the square-root filtering methods, since the methods guarantee, that the difference between two positive definite matrices and the result are positive definite matrices. Also, the square-root filtering suppresses the negative effect of errors caused by insumcient length of computers bit word, rounding, etc., which leads to the loss of numerical stability of the algorithm and also to the loss of positive definiteness of the matrices. The described methodology is being used to create continuous identification forgetting and weighting algorithms. These algorithms are used for long-term identification and creation of mathematical models of the monitored industrial systems. The obtained models are then being used for various applications, mostly for applications which require predictive control.