Joint Parameter and State Estimation for Input‐Nonlinear State‐Space Models With Random Data Missing Based on Kalman Smoothing

The state‐space models are often used to describe the characteristics of many physical or chemical processes, but unknown system parameters bring difficulties to the solution of the state equation. This paper addresses the challenge of accurate parameter and state estimation for input‐nonlinear state‐space models with random missing data. To tackle this issue, an expectation‐maximization‐based Kalman smoothing (EM‐KS) algorithm is derived by transforming the state‐space models into the form of a pseudo‐linear equation. The unknown intermediate states are obtained through KS. In the pseudo‐linear equation, all unknown parameters are treated as a vector and estimated under the framework of the EM algorithm. By treating the missing data as latent variables, the proposed algorithm ingeniously avoids the missing data points and can obtain effective parameter estimation even in the case of a high data missing ratio. Simulation results demonstrate the effectiveness of the proposed method, while comparison with the existing approach further demonstrates its reliability.