abstractabstractThe authors present an adaptive identification method (AIM) primarily for adaptive control systems with insufficient persistent excitation. In this paper, the matrix P(t-l) resetting, a new forgelling ...
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abstractabstractThe authors present an adaptive identification method (AIM) primarily for adaptive control systems with insufficient persistent excitation. In this paper, the matrix P(t-l) resetting, a new forgelling factor λ(1), remembering units, and a weighted filtering algorithm are proposed. The AIM technique, using a modified leastsquaresalgorithm, is presented in terms of the previously mentioned procedures. Theoretical analyses and simulation results demonstrate that the proposed methodology can overcome the bursting problems thaI sometimes exisl in adaptive control systems.
The splitted generalized LeRoux-Gueguen algorithm performs a least-squares estimate of autoregressive parameters. Due to its lattice structure and finite memory length it seems to be well suited to fixed-point arithme...
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The splitted generalized LeRoux-Gueguen algorithm performs a least-squares estimate of autoregressive parameters. Due to its lattice structure and finite memory length it seems to be well suited to fixed-point arithmetic implementation. In the present paper the effect of round-off errors caused by such implementation is studied. This is done by computer simulation of the fixed-point implementation with varying wordlengths for characteristic quantities and comparison with a floating-point implementation as a reference. Input signals are determined by pole trajectories of the transfer functions of their autoregressive model filters. Comparison between the two implementations is carries out by a likelihood ratio. The simulation results lead to empirical guidelines for the choice of wordlengths.
The numerical properties of implementations of the recursive least-squares identification algorithm are of great importance for their continuous use in various adaptive schemes. Here we investigate how an error that i...
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The numerical properties of implementations of the recursive least-squares identification algorithm are of great importance for their continuous use in various adaptive schemes. Here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates. It is shown that conventional LS algorithms, including Bierman's UD-factorization algorithm are exponentially stable with respect to such errors, i.e. the effect of the error decays exponentially. The base of the decay is equal to the forgetting factor. The same is true for fast lattice algorithms. The fast least-squares algorithm, sometimes known as the ‘fast Kalman algorithm’ is however shown to be unstable with respect to such errors.
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