In this paper, we extend the modulating functions method to estimate the state and the unknown input of a linear time-varying system defined by a linear differential equation. We first estimate the unknown input by ta...
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In this paper, we extend the modulating functions method to estimate the state and the unknown input of a linear time-varying system defined by a linear differential equation. We first estimate the unknown input by taking a truncated Jacobi orthogonal series expansion with unknown coefficients which can be estimated by the modulating functions method. Then, we estimate the state by using extended modulatingfunctions and the estimated input. Both input and state estimators are given by exact integral formulae involving modulatingfunctions and the noisy output. Hence, estimations at different instants can be non-asymptotically obtained using a sliding window of finite length. Numerical results are given to show the accuracy and the robustness of the proposed estimators against corrupting noises.
The modulating functions method is a very effective method for parameter estimation of continuous-time systems that are linear in their parameters. One efficient implementation developed by Pearson and Lee involves th...
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The modulating functions method is a very effective method for parameter estimation of continuous-time systems that are linear in their parameters. One efficient implementation developed by Pearson and Lee involves the use of trigonometric functions and fast computations offered by FPT techniques. In this paper, a recursive implementation of the method is developed for on-line parameter estimation of a continuous-time system by shifting a fixed window of time series data one step forward at each sampling instant. The resulting recursion algorithms are fast, and use the identities of discrete Fourier transforms along with some inherent commutative properties. A simulation example with a Van der Pol oscillator is included to investigate the performance of the proposed estimation method. (C) 1997 Elsevier Science Ltd.
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