Parameter Estimation Using the Smoother

The problem of the parameter estimation in the discrete-time system is considered by the use of the argorithm of the smoothing which is developed by Meditch. The main approach is estimating the new vector combined with the states and the unknown parameters making use of the smoother, but it is not possible to apply the combined vector directly to it, because of the limitation of the smoother where the noise covariance matrices are assumed to be positive definite. Adding the imaginary independent Gaussian noise with zero mean to the unknown parameter vector, the smoother applies to the parameter estimation. As a numerical example, the parameter estimation of the first-order nonlinear system is examined.