Recursive Least-squares Identification Algorithm Research Articles

Fixed-lag smoothing in the identification of time-varying systems with unknown dead time

This paper considers a new application of fixed-lag smoothing algorithms for identification. It could be used online in conjunction with the extended recursive least-squares identification algorithm. This offers a scheme for identifying time-varying process models with unknown dead time from sampled input-output records. Application to short records with time-varying dynamics, where recursive algorithms without smoothing may not give a clear indication of the time variation, is of particular interest. Optimal Kalman-filter and fixed-lag smoothing algorithms are reviewed, and their computational requirements and stability in an identification context are examined. The most attractive measures of model structure obtained from identification algorithms are tested on artificial and real records. It is concluded that the innovation and adjoint variables are feasible and effective indicators for identifying model structure goodness.

Error propagation properties of recursive least-squares adaptation algorithms

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.