SOME POSSIBILITIES FOR IMPLEMENTING THE KALMAN FILTER IN COMPUTATIONAL ALGORITHMS

V. M. Bobrov, V. M. Kukhtin, V. М. Chekshin
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1988. Вып.3. С. 17-20.

      Possibilities are considered for implementing the Kalman filter in computational algorithms which use difference schemes. A new approach relies upon assuming stochastic properties of the numerical solution error and a possibility for using a filtering to improve this solution. A problem formulation is given and several filtering algorithm versions are presented. Examples of linear heat conduction and transport equations as well as a nonlinear diffusion equation are considered. The results show that filtering may substantially improve the numerical solution.