Remarks on the mean square tracking error

The purpose of this paper is to extend recent results of Ljung and Priouret to a more general class of regressors.     

Performance analysis of general tracking algorithms

A general family of tracking algorithms for linear regression models is studied. It includes the familiar least mean square gradient approach, recursive least squares, and Kalman filter based estimators. The exact expressions for the quality of the obtained estimates are complicated. Approximate, and easy-to-use, expressions for the covariance matrix of the parameter tracking error are developed. These are applicable over the whole time interval, including the transient, and the approximation error can be explicitly calculated     

Nonlinear black-box modeling in system identification: a unified overview

A nonlinear black-box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area, with structures based on neural networks, radial basis networks, wavelet networks and hinging hyperplanes, as well as wavelet-transform-based methods and models based on fuzzy sets and fuzzy rules. This paper describes all these approaches in a common framework, from a user's perspective. It focuses on what are the common features in the different approaches, the choices that have to be made and what considerations are relevant for a successful system-identification application of these techniques. It is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space. These mappings are discussed separately. The latter mapping is usually formed as a basis function expansion. The basis functions are typically formed from one simple scalar function, which is modified in terms of scale and location. The expansion from the scalar argument to the regressor space is achieved by a radial- or a ridge-type approach. Basic techniques for estimating the parameters in the structures are criterion minimization, as well as two-step procedures, where first the relevant basis functions are determined, using data, and then a linear least-squares step to determine the coordinates of the function approximation. A particular problem is to deal with the large number of potentially necessary parameters. This is handled by making the number of ‘used’ parameters considerably less than the number of ‘offered’ parameters, by regularization, shrinking, pruning or regressor selection.     

Infrared absorption in Li-intercalated tungsten oxide

Thin films of amorphous and polycrystalline tungsten oxide were produced by reactive dc magnetron sputtering and nanocrystalline films were deposited by advanced gas evaporation. The films were submitted to electrochemical intercalation of Li ions before infrared reflectance measurements were carried out. For crystalline films, the reflectance in the wavelength region 10–30 μm increases upon intercalation, indicating an increasing free-electron contribution. On the other hand, all the films display an increased absorption at wavelengths less than 10 μm when intercalated. The thermal emittance could be varied from about 0.5 to 0.7–0.75 by intercalation in films with thicknesses in excess of 1 μm. Both absorption and interference contribute to the emittance contrast.     

Performance analysis of the forgetting factor RLS algorithm

An analysis is given of the performance of the standard forgetting factor recursive least squares (RLS) algorithm when used for tracking time-varying linear regression models. Three basic results are obtained: (1) the ‘P-matrix’ in the algorithm remains bounded if and only if the (time-varying) covariance matrix of the regressors is uniformly non-singular; (2) if so, the parameter tracking error covariance matrix is of the order O(μ + γ²/μ), where μ = 1 - λ, λ is the forgetting factor and γ is a quantity reflecting the speed of the parameter variations; (3) this covariance matrix can be arbitrarily well approximated (for small enough μ) by an expression that is easy to compute.     

Issues in sampling and estimating continuous-time models with stochastic disturbances

The standard continuous time state space model with stochastic disturbances contains the mathematical abstraction of continuous time white noise. To work with well defined, discrete time observations, it is necessary to sample the model with care. The basic issues are well known, and have been discussed in the literature. However, the consequences have not quite penetrated the practice of estimation and identification. One example is that the standard model of an observation, being a snapshot of the current state plus noise independent of the state, cannot be reconciled with this picture. Another is that estimation and identification of time continuous models require a more careful treatment of the sampling formulas. We discuss and illustrate these issues in the current contribution. An application of particular practical importance is the estimation of models based on irregularly sampled observations.     

Difference algebra and system identification

The framework of differential algebra, especially Ritt’s algorithm, has turned out to be a useful tool when analyzing the identifiability of certain nonlinear continuous-time model structures. This framework provides conceptually interesting means to analyze complex nonlinear model structures via the much simpler linear regression models. One difficulty when working with continuous-time signals is dealing with white noise in nonlinear systems. In this paper, difference algebraic techniques, which mimic the differential-algebraic techniques, are presented. Besides making it possible to analyze discrete-time model structures, this opens up the possibility of dealing with noise. Unfortunately, the corresponding discrete-time identifiability results are not as conclusive as in continuous time. In addition, an alternative elimination scheme to Ritt’s algorithm will be formalized and the resulting algorithm is analyzed when applied to a special form of the nfir model structure.     

Amperometric biosensor for formic acid in air

The possibility of developing a simple, inexpensive and specific personal passive “real-time” air sampler incorporating a biosensor for formic acid was investigated. The sensor is based on the enzymatic reaction between formic acid and formate dehydrogenase (FDH) with nicotinamide adenine dinucleotide (NAD⁺) as a co-factor and Meldola's blue as mediator. An effective way to immobilise the enzyme, co-factor and Meldola's blue on screen-printed, disposable, electrodes was found to be in a mixture of glycerol and phosphate buffer covered with a gas-permeable membrane. Steady-state current was reached after 4–15 min and the limit of detection was calculated to be below 1 mg/m³. However, the response decreased by 50% after storage at −15°C for 1 day.     

A constraint-based variability modeling framework

Constraint-based variability modeling is a flexible, declarative approach to managing solution-space variability. Product variants are defined in a top-down manner by successively restricting the admissible combinations of product artifacts until a specific product variant is determined. In this paper, we illustrate the range of constraint-based variability modeling by discussing two of its extreme flavors: constraint-guarded variability modeling and constraint-driven variability modeling. The former applies model checking to establish the global consistency of product variants which are built by manual specification of variations points, whereas the latter uses synthesis technology to fully automatically generate product variants that satisfy all given constraints. Each flavor is illustrated by means of a concrete case study.