A square-root method for identifying the parameters of discrete-time linear stochastic systems with unknown input signals

The paper proposes a new square-root gradient-based parameter identification method for discrete-time linear stochastic state-space systems with unknown input signals. A new algorithm is developed for calculating the values of the identification criterion and its gradient. The approach is based on a square-root modification of the Gillijns – De Moor method and uses numerically stable matrix orthogonal transformations. Unlike the existing solutions, this paper uses original methods for differentiating matrix orthogonal transformations. A new sensitivity model is constructed and theoretically justified, that allows calculating the values of the identification criterion gradient by using partial derivatives of state vector estimates based on identified parameters. The main results include new equations for the square-root sensitivity model and a square-root algorithm for calculating the values of the identification criterion and its gradient. Numerical experiments were performed in MATLAB for example of solving the numerical identification problem of a stochastic diffusion model with unknown boundary conditions. The effectiveness of the proposed algorithm is confirmed by comparison of gradient-based and gradient-free methods. The results of numerical experiments demonstrate efficiency of approach proposed which can be used to solve practical problems of identifying the parameters of mathematical models represented by discrete-time state-space linear stochastic systems, in the absence of any prior information about the input signals.