Search

This paper studies the joint state and parameter estimation problem for a linear state space system with time-delay. A multi-innovation gradient algorithm is developed based on the Kalman filtering principle. To improve the convergence rate, a filtering based multi-innovation gradient algorithm is proposed by using the filtering technique. The analysis indicates that the parameter estimates given by the proposed algorithms converge to their true values under the persistent excitation conditions. A simulation example is given to confirm that the proposed algorithms are effective. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers connections between the cost functions of some parameter identification methods for system modelling, including the well known projection algorithm, stochastic gradient (SG) algorithm and recursive least squares (RLS) algorithm, and presents a modified SG algorithm by introducing the convergence index and a multi-innovation projection algorithm, a multi-innovation SG algorithm and a multi-innovation RLS algorithm by introducing the innovation length, aiming at improving the convergence rate of the SG and RLS algorithms. Furthermore, this paper derives an interval-varying multi-innovation SG and an interval-varying multi-innovation RLS algorithm in order to deal with missing data cases. [Copyright &y& Elsevier]

Abstract: This paper presents a new technique for designing IIR filters that have minimum deviation from equiripple response. The algorithm is also able to find transfer functions with unequal numerator and denominator orders, which are suitable for both digital and analog IIR sampled-data realizations. Elliptic filters are produced as a particular case, when equal numerator and denominator orders are specified. Pole-zero mapping is used for scalar update of optimization parameters, thereby reducing the algorithm complexity. Zeros are structurally allocated on the unit circumference for efficient stopband shaping. Moreover, filter stability is easily enforced by restricting the radii of the poles to be lower than 1. A Taylor series expansion is employed to determine the step size of the parameter updates. The proposed approach is based on evaluations of partial cost functions to avoid local minima, and hence increase the robustness and the convergence rate of the optimization process. Design examples are shown to illustrate the efficacy of the proposed design technique, compared to alternative design techniques. [Copyright &y& Elsevier]

Abstract: This paper considers the identification problems of the Hammerstein nonlinear systems. A projection and a stochastic gradient (SG) identification algorithms are presented for the Hammerstein nonlinear systems by using the gradient search method. Since the projection algorithm is sensitive to noise and the SG algorithm has a slow convergence rate, a Newton recursive and a Newton iterative identification algorithms are derived by using the Newton method (Newton–Raphson method), in order to reduce the sensitivity of the projection algorithm to noise, and to improve convergence rates of the SG algorithm. Furthermore, the performances of these approaches are analyzed and compared using a numerical example, including the parameter estimation errors, the stationarity and convergence rates of parameter estimates and the computational efficiency. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a novel identification algorithm for a class of dual-rate sampled-data systems whose input–output data are measured by two different sampling rates. A polynomial transformation technique is employed to derive a mathematical model for such dual-rate systems. The proposed modified stochastic gradient algorithm has faster convergence rate than stochastic gradient algorithms for parameter identification using the dual-rate input–output data. Convergence properties of the algorithm are analyzed. Finally, illustrative and comparison examples are provided to verify the effectiveness and performance improvement of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper combines the multi-innovation identification theory and the auxiliary model identification idea and presents an auxiliary model based multi-innovation stochastic gradient algorithm by expanding the scalar innovation to an innovation vector and introducing the innovation length. Convergence analysis in the stochastic framework indicates that the parameter estimates given by the proposed algorithm can fast converge to their true values. Finally, we illustrate and test the proposed algorithm with an example. [Copyright &y& Elsevier]