Algorithms for the synthesis of dynamic object control systems significantly use the
concepts of dynamic Kalman filtration. An iterative algorithm for estimating adaptive filters in a
dynamic object control system is presented. For the system of linear equations, the optimal
algorithm for evaluating the Kalman filter and the calculation scheme are given. The Kalman filter
uses measurements a state vector estimate and the corresponding estimation error covariance
matrix. At the same time, an iterative algorithm for calculating the gain of the Kalman filter is proposed. The considered iterative algorithms are based on the available a priori information, in
particular, on the error of the initial data, to select from the entire sequence some approximation
that is sufficiently close to the original solution.
Algorithms for the synthesis of dynamic object control systems significantly use the
concepts of dynamic Kalman filtration. An iterative algorithm for estimating adaptive filters in a
dynamic object control system is presented. For the system of linear equations, the optimal
algorithm for evaluating the Kalman filter and the calculation scheme are given. The Kalman filter
uses measurements a state vector estimate and the corresponding estimation error covariance
matrix. At the same time, an iterative algorithm for calculating the gain of the Kalman filter is proposed. The considered iterative algorithms are based on the available a priori information, in
particular, on the error of the initial data, to select from the entire sequence some approximation
that is sufficiently close to the original solution.
| № | Author name | position | Name of organisation |
|---|---|---|---|
| 1 | Sevinov J.U. | teacher | TSTU |
| 2 | Zaripov O.O. | teacher | TSTU |
| 3 | Zaripova S.O. | teacher | TSTU |
| № | Name of reference |
|---|---|
| 1 | A.A. Krasovsky. Handbook on the theory of automatic control. Moscow “Science”, 1987. 712. |
| 2 | V.N. Afanasyev. Dynamic control systems with incomplete information: Algorithmic construction. “Publishing House”, 2007. |
| 3 | M.V. Kolos., I.V. Kolos. Linear optimal filtration methods. – Moscow: “Science”, 2000. 158. |
| 4 | M.A. Ogarkov. Methods for statistical evaluation of random process parameters. Moscow: “Energo atom publishing house”, 1990. 208. |
| 5 | S.V. Pervachev., A.I. Perov. Adaptive message filtering. Moscow: “Radio and Communications”, 1991. 160. |
| 6 | J.U. Sevinov., O.O. Zaripov., S.O. Zaripova. The algorithm of adaptive estimation in the synthesis of the dynamic objects control systems. International journal of advanced science and technology. “Special Issue”, 2020. 1096. |
| 7 | H.Z. Igamberdiyev., A.N. Yusupbekov., O.O. Zaripov., J.U. Sevinov. Algorithms of adaptive identification of uncertain operated objects in dynamical models. “Procedia Computer Science”, 2017. 854. |
| 8 | N.R. Yusupbekov., H.Z. Igamberdiev., O.O. Zaripov., U.F. Mamirov. Stable iterative neural network training algorithms based on the extreme method. “Advances in intelligent systems and computing”, 2021. 246. |
| 9 | B.D.O. Anderson., J.B.Moore. “Optimal filtering, dover publications”, New York, USA, 2005. |
| 10 | N. Assimakis., M. Adam. Global systems for mobile position tracking using Kalman and Lainiotis filters. “The Scientific World Journal”, 2014. 8. |
| 11 | N. Assimakis., M.Adam. Iterative and algebraic algorithms for the computation of the steady state kalman filter gain. “Hindawi publishing corporation, applied mathematics”, 2014. 10. |
| 12 | N. Assimakis., M.Adam. Kalman filter Riccati equation for the prediction, estimation and smoothing error covariance matrices. “ISRN computational mathematics”, 2013. 7. |
| 13 | J.R.P. de Carvalho., E.D. Assad., H.S. Pinto. Kalman filter and correction of the temperatures estimated by precis model. “Atmospheric Research”, 2011. 218. |
| 14 | R. Furrer., T.Bengtsson. Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants. “Journal of multivariate analysis”, 2007. 227. |
| 15 | R.A. Horn., C.R. Johnson. Matrix analysis. “Cambridge University Press”, Cambridge, UK, 2005. |
| 16 | Vasiliev F.P. Optimization methods. “Publishing House: Factorial Press”, 2002. 824. |
| 17 | A.B. Bakushinsky., M.Y. Kokurin. Iterative methods of solving irregular equations. Moscow: “Lenand”, 2006. 214. |