‘Quasi-OBE’ (QOBE) is an adaptive set identification and filtering algorithm which is based on the principles of optimal bounding ellipsoid processing, but which has other geometric and classic least-squares interpretations which greatly enhance its application potential. In particular, because of its unusual optimization criterion, the ellipsoidal membership set associated with QOBE is more likely to retain (i.e. to move in the parameter space with) the system model's ‘true parameters, ’ say θ*, when those parameters are time varying. Moreover, in the unlikely event that θ* moves outside the set, the integrity of the point-set estimation remains intact, and the estimator provably converges under known conditions. The consistency of the set estimation can be restored at any time using typical ‘rescue procedures’ if desired. Understanding convergence performance is very critical to successful QOBE application. Convergence analysis of both the central point estimate and measures of the hyperellipsoidal membership set is presented. The main results give conditions for point estimate convergence, and show that set convergence to a point is not possible. Implications of these convergence results for practical application are discussed. Copyright © 2007 John Wiley & Sons, Ltd.

Convergence analysis of the quasi-OBE algorithm and related performance issues

At ChinaSIP 2013, Yan et al. presented a new method for identification of system models that are linear in parametric structure, but arbitrarily nonlinear in signal operations. The strategy blends traditional system identification methods with three modeling strategies that are not commonly employed in signal processing: linear-time-invariant-in-parameters models, set-based parameter identification, and evolutionary selection of the model structure. This paper reports recent advances in the theoretical foundation of the methods, then focuses on the operation and performance of the approach, particularly the evolutionary model determination. This work opens the door to the use of a broadly generalized class of models with applicability to many contemporary signal processing problems.

Evolutionary model selection for identification of nonlinear parametric systems

Ellipsoidal approximation of the ellipsoid and hyperlayer crossing has been considered as a basis of the algorithm of states estimation of the linear controlled system whose set of possible states is represented with an ellipsoid, and observations – with a hyperlayer. This representation is considered as an analogue of Kalman filter. The conditions of a priori system state and a posteriori measurement information compatibility and sensitivity of the algorithm to a choice of its parameters have been investigated. Dependence of the system state estimate improvement on a relative width of the hyperlayer of a set of observations has been shown. The obtained algorithm in comparison with the known solutions at minor degradation of accuracy is much easier in realization and stabler in operation from the standpoint of prior guesses violation.

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Development of the guaranteed estimation robust algorithm of linear controlled system states

This paper presents a new method for identification of system models that are linear in parametric structure, but arbitrarily nonlinear in signal operations. The strategy blends traditional system identification methods with three modeling strategies that are not commonly employed in signal processing: linear-time-invariant-in-parameters models, set-based parameter identification, and evolutionary selection of the model structure. This paper reports recent advances in the theoretical foundation of the methods, then focuses on the operation and performance of the approach, particularly the evolutionary model determination. The method is applied to the modeling of microbial growth by Monod Kinetics.

Biologically-motivated system identification: application to microbial growth modeling.

Well documented adaptive properties of quasi-optimal bounding ellipsoid (QOBE) algorithms depend on the choices of error bound. Such dependency becomes particularly noticeable in QOBE linear parameter estimation of speech signals. Vowel classification, for example, would therefore stands to benefit from the efficiency of QOBE algorithms. This paper discusses tradeoffs in error bound estimation and presents related experiments and simulations.

Estimating the error bound in QOBE Vowel classification

Optimal bounding ellipsoid (OBE) identification algorithms are noted for their simplicity and ability to leverage model error-bound knowledge for improved parameter convergence. However, the OBE convergence rate is dependent on the pointwise "tightness" of the model error-bound estimates. Since the least upper bound on the model error is often unknown, the convergence rate is compromised by the need to overestimate error-bounds lest the integrity of the process be violated by underestimation. We present an effective under-bounding safeguard against system model violations in OBE processing. Simulation examples in state estimation and speech processing demonstrate the efficacy of the under-bounding safeguard.

J.R. Deller

Papers

Adaptive optimal bounded-ellipsoid identification with an error under-bounding safeguard: applications in state estimation and speech processing