In system identification, the error evolution is composed of two decoupled parts: one is the identifying information on the current estimation residual, while the other is past arithmetic errors. Previous recursive algorithms only considered how to update current prediction errors. Up to now, research has mostly been based on recursive least-squares (RLS) methods. In this note, a general recursive identification method is proposed for discrete systems. Using this new algorithm, a recursive empirical frequency-domain optimal parameter (REFOP) estimate is established. The REFOP method has the advantage of resisting disturbance noise. Some simulations are included to illustrate the new method's reliability.

Recursive estimation methods for discrete systems

We establish an equivalence between two conceptually different methods of signal estimation under modeling uncertainty, viz., set-theoretic (ST) estimation and maximum entropy (maxent) MAP estimation. The first method assumes constraints on the signal to be estimated, and the second assumes constraints on a probability distribution for the signal. We provide broad conditions under which these two estimation paradigms produce the same signal estimate. We also show how the maxent formalism can be used to provide solutions to three important problems: how to select sizes of constraint sets in ST estimation (the analysis highlights the role of shrinkage); how to choose the values of parameters in regularized restoration when using multiple regularization functionals; how to trade off model complexity and goodness of fit in a model selection problem.

On the equivalence of set-theoretic and maxent MAP estimation

Most system recursive identification algorithms are based on the prediction error (PE) criterion. Such a recursive algorithm only considers the present estimation residual error instead of all estimation residuals. It would result in large estimation error when the signal noise disturbs strongly. In this paper, a new identification criterion is proposed. It considers both the errors between the actual outputs and the estimation result and the difference of each estimation error. Under this criterion, a new recursive algorithm MSDCN (Multi-dimensional System Disturbed by Color Noise) is proposed. For multi-dimensional systems, weighting different values on the estimation errors and the difference of each error, MSDCN could both decrease the estimation errors and got smooth prediction curves. Several simulation examples are given to illustrate the method’s anti-disturbance performance.

Identification of multi-dimensional system based on a novel criterion

A new identification criterion is concerned for disturbed system with color noise in this paper. The cost function considers both the errors between the actual outputs and the estimation result and the difference of each estimation error. Under this performance function, a new recursive algorithm DSCN (Disturbed System with Color Noise) is proposed. It could reduce the influence of noise in system identification, further decrease the prediction error. Several simulation examples are given to illustrate the method's anti-disturbance performance.

Recursive Algorithms for a Novel Identification Criterion

A new algorithm for estimation of a linear-in-parameters model is developed and tested by simulation. The method is based on the assumption of independent, identically distributed noise samples with a triangular density function. Such a noise model well approximates the symmetrically distributed sources of noise frequently encountered in practice, and the inclusion of a distribution assumption allows the computation of a pseudo-mean estimate to complement the set solution. The proposed algorithm recursively incorporates incoming observations with decreasing computational complexity as the number of updates increases. Simulations demonstrate that the algorithm has very favorable convergence rates and estimation accuracy and is very robust to deviations from the assumed noise properties. Comparisons with other set-theoretic algorithms and with conventional RLS are given.

Y.C. Tsai

Papers

Set-theoretic estimation based on a priori knowledge of the noise distribution