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IQML-like algorithm and inverse iteration algorithm in dynamic system identification

The Structured Total Least Squares (STLS) problem is an extension of the Total Least Squares (TLS) problem for solving an overdetermined system of equations Ax ≈ b. The Dynamic Total Least Squares (DTLS) problem is a special case of STLS problem. In this paper, we illustrate the TLS singular value problem by defining some vectors from a new viewpoint. And we also derive the DTLS nonlinear singular value problem by this new viewpoint. Futhermore, we introduce a heuristic Iterative Quadratic Maximum Likelihood (IQML)-like algorithm for solving DTLS nonlinear problem. The main objective of this paper is to compare the difference between this variety of IQMLlike algorithm and the Inverse Iteration algorithm for solving the DTLS nonlinear singular value problem by simulation experiments with some conditions. The simulation results show that the convergence rate of IQML-like algorithm is faster than that of Inverse Iteration algorithm under the same conditions and the computational efficiency of the IQML-like algorithm is also higher compared with the Inverse Iteration algorithm.