Joint state filtering and parameter estimation for linear stochastic time-delay systems

This paper presents the joint state filtering and parameter estimation problem for linear stochastic time-delay systems with unknown parameters. The original problem is reduced to the mean-square filtering problem for incompletely measured bilinear time-delay system states over linear observations. The unknown parameters are considered standard Wiener processes and incorporated as additional states in the extended state vector. To deal with the new filtering problem, the paper designs the mean-square finite-dimensional filter for incompletely measured bilinear time-delay system states over linear observations. A closed system of the filtering equations is then derived for a bilinear time-delay state over linear observations. Finally, the paper solves the original joint estimation problem. The obtained solution is based on the designed mean-square filter for incompletely measured bilinear time-delay states over linear observations, taking into account that the filter for the extended state vector also serves as the identifier for the unknown parameters. In the example, performance of the designed state filter and parameter identifier is verified for a linear time-delay system with an unknown multiplicative parameter over linear observations.