Computation optimization procedures for stochastic filtering and smoothing algorithms via Kalman filter

Filtering and smoothing procedures based on the Kalman filter are significantly used in engineering and economic tasks to evaluate the state vector of linear dynamic systems in noisy data conditions. Kalman filtering is an important section in the theory of control system design. The efficiency, accuracy and speed of stochastic filtering and smoothing algorithms are largely determined by the analytical and numerical algorithms used to perform computational procedures. Within the framework of this article, several numerical algorithms are proposed aimed at optimizing Kalman filtering and smoothing procedures.