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Powered Air Purifying Respirator (PAPRs) are respirators that utilise a small centrifugal blower to aid in drawing air through a filter. If the dynamic behaviour of PAPRs with filters can be modelled, adaptive controllers can be made so that air is only supplied through the filter when a user inhales. This paper presents the identification of a Wiener model using a separable least squares method with experimental application to a PAPR. The linear dynamics are shown to fit to an output error model structure, with the nonlinearity being a quadratic function. The model structure is then validated on a PAPR constructed in open loop formation. The validation is furthered by altering the filter resistance to check the performance of the model.

Time series from Landsat and Sentinel-2 satellites have great potential for modeling vegetation seasonality. However, irregular time sampling and frequent data loss due to clouds, snow, and short growing seasons, makes this modeling a challenge. We describe a new method for modeling seasonal vegetation index dynamics from satellite time series data. The method is based on box constrained separable least squares fits to logistic model functions combined with seasonal shape priors. To enable robust estimates, we extract a base level (i.e., the minimum dormant season value) from the frequency distribution of clear-sky vegetation index values. A seasonal shape prior is computed from several years of data, and in the final fits local parameters are box constrained. More specifically, if enough data values exist in a certain time period, the corresponding local parameters determining the shape of the model function over this period are relaxed and allowed to vary freely. If there are no observations in a period, the corresponding local parameters are locked to the parameters of the shape prior. The method is flexible enough to model interannual variations, yet robust enough when data are sparse. We test the method with Landsat, Sentinel-2, and MODIS data over a forested site in Sweden, demonstrating the feasibility and potential of the method for operational modeling of growing seasons.

In this paper, the Hammerstein identification problem with correlated inputs is studied in a prediction error framework using separable least squares methods. Thus, the identification is recast as an optimization over the parameters used to describe the nonlinearity. A sufficient condition is derived that guarantees that the identification problem is quasiconvex with respect to the parameters that describe the nonlinearity. Simulations using both IID and correlated inputs are used to illustrate the result.

International audience; This paper deals with the identification of Wiener models that involve backlash operators bordered by possibly noninvertible parametric lines. The latter are also allowed to cross each other making possible to account for general-shape static nonlinearities. The linear dynamic subsystem is not-necessarily parametric but is BIBO stable. A frequency identification method is developed that provides estimates of the nonlinear operator parameters as well as estimates of the linear subsystem frequency gain. The method involves standard and separable least squares estimators that all are shown to be consistent. Backlash operators and memoryless nonlinearities are handled within a unified framework.

Ph.D. Programs Foundation of Ministry of Education of China [20100121120020]; Major Science and Technology Special Project of Fujian Province, China [2009HZ0003-1]

The Hammerstein identification problem is studied using a prediction error method in a separable least squares framework. Thus, the identification is recast as an optimization over the parameters used to describe the nonlinearity. Under certain conditions the identification problem is quasiconvex. First, the identification problem is shown to be quasiconvex under certain assumptions, including the use of an IID input. Next, the IID requirement is relaxed, and a sufficient condition for quasiconvexity is derived. The results are illustrated using a series of simulations.

The stiction of control valve is one of main causes which make control loop instable in the process industry. Now a number of studies on the diagnosis of control valves are based on stiction. It needs developing a proper method which can detect, quantify, and compensate stiction. A non-invasive method has been used into the fault diagnosis for stiction of pneumatic control valve. Firstly, a two-parameter data-driven model about stiction has been established, and on the basis of separable least squares method, combined with the global search algorithm to deduce the model identification method. Secondly, ellipse fitting method has been adopt to confirm whether the stiction existed, thus the stiction could be quantified, and on this basis, the stiction was compensated. So it improved the performance of control system. Thirdly, the validity of the method was confirmed by simulation.

This note compares and contrasts the non-linear parameter varying (NLPV) and state-dependent parameter (SDP) model classes. It shows that, while they have similarities, the two-stage SDP modelling procedure, involving non-parametric identification, followed by parametric estimation, is quite different from the single stage NLPV procedure. In particular, the SDP procedure allows for the identification of the model structure and the nature of the non-linearities, prior to the estimation of the parameters that characterize this identified model structure. In contrast to NLPV modelling, therefore, SDP estimation opens up the ‘black box’ and reveals the inner nature of the non-linear system.

In this paper, the parametrization of state-space systems by data driven local coordinates as introduced by (McKelvey et al., 2003) is modified. This modification leads to an alternative analogous parametrization which can be used for a suitable concentrated likelihood-type criterion function, where the concentration step can be done by a generalized least squares step. An obvious consequence is the reduced number of parameters resulting in less computational burden, but, of course, the criterion function itself is changed by the concentration step. The resulting new parametrization is called slsDDLC, and its topological and geometrical properties are investigated in detail.

We consider the least squares approximation of gridded 2D data by tensor product splines with free knots. The smoothing functional to be minimized—a generalization of the univariate Schoenberg functional—is chosen in such a way that the solution of the bivariate problem separates into the solution of a sequence of univariate problems in case of fixed knots. The resulting optimization problem is a constrained separable least squares problem with tensor product structure. Based on some ideas developed by the authors for the univariate case, an efficient method for solving the specially structured 2D problem is proposed, analyzed and tested on hand of some examples from the literature.

In this paper, a sensitivity analysis is carried out for the problem of simultaneous estimation of induction motor's state and parameters. This is done using separable least squares formulation. It comes out that even in the presence of persistent excitations, the above problem is very sensitive to noises and/or uncertainties especially for one of the four possibly identifiable combinations of parameters. Numerical experiments are conducted that confirm the a priori sensitivity-based predictions.

Shooter localization systems are used to detect and locate the origin of gunfire. A wireless sensor network is one possible implementation of such a system. A wireless sensor network is sensitive to synchronization errors. Localization techniques that rely on the timing will give less accurate or even useless results if the synchronization errors are too large. This thesis focuses on the influence of synchronization errors on the abilityto localize a shooter using a wireless sensor network. A localization algorithm is developed and implemented and the effect of synchronization errors is studied. The localization algorithm is evaluated using numerical experiments, simulations, and data from real gunshots collected at field trials. The results indicate that the developed localization algorithm is able to localizea shooter with quite good accuracy. However, the localization performance is to a high degree influenced by the geographical configuration of the network as well as the synchronization error. Skottlokaliseringssystem används för att upptäcka och lokalisera ursprunget för avlossade skott. Ett trådlöst sensornätverk är ett sätt att utforma ett sådant system.Trådlösa sensornätverk är känsliga för synkroniseringsfel. Lokaliseringsmetoder som bygger på tidsobservationer kommer med för stora synkroniseringsfel ge dåliga eller helt felaktiga resultat. Detta examensarbete fokuserar på vilken inverkan synkroniseringsfel har på möjligheterna att lokalisera en skytt i ett trådlöst sensornätverk. En lokaliseringsalgoritm utvecklas och förmågan att korrekt lokalisera en skytt vid olika synkroniseringsfel undersöks. Lokaliseringsalgoritmen prövas med numeriska experiment, simuleringar och även för data från riktiga skottljud, insamlade vid fältförsök. Resultaten visar att lokaliseringsalgoritmen fungerar tillfredställande, men att lokaliseringsförmågan till stor del påverkas av synkroniseringsfel men även av sensornätverkets geografiska utseende.

This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University. In this work we address the problem of identifying a discrete-time nonlinear system composed of a linear dynamical system connected to a static nonlinear component. We use linear fractional representation to provide a united framework for the identification of two classes of such systems. The first class consists of discrete-time systems consists of a linear time invariant system connected to a continuous nonlinear static component. The identification problem of estimating the unknown parameters of the linear system and simultaneously fitting a math order spline to the nonlinear data is addressed. A simple and tractable algorithm based on the separable least squares method is proposed for estimating the parameters of the linear and the nonlinear components. We also provide a sufficient condition on data for consistency of the identification algorithm. Numerical examples illustrate the performance of the algorithm. Further, we examine a second class of systems that may involve a nonlinear static element of a more complex structure. The nonlinearity may not be continuous and is approximated by piecewise a±ne maps defined on different convex polyhedra, which are defined by linear combinations of lagged inputs and outputs. An iterative identification procedure is proposed, which alternates the estimation of the linear and the nonlinear subsystems. Standard identification techniques are applied to the linear subsystem, whereas recently developed piecewise affine system identification techniques are employed for the estimation of the nonlinear component. Numerical examples show that the proposed procedure is able to successfully profit from the knowledge of the interconnection structure, in comparison with a direct black box identification of the piecewise a±ne system. Funding was obtained as a Marie Curie Early Stage Researcher Training fellowship, under the NET-ACE project (MEST-CT-2004-6724).

The aim of this paper is to propose a novel identification aalgorithm based on separable least squares ideas, for a class of nonlinear, possibly parameter-varying, input/output models. These models are given in the form of a Linear Fractional Transformation (LFT) where the "forward" part is represented by a conventional linear regression and the "feedback" part is given by a nonlinear map which can take into account scheduling variables available for measurement. The nonlinear part of the model can be parameterised according to various paradigms, like, e.g., Neural Network (NN) or NARX.

Designing estimators based on low rank signal models is a common practice in signal processing. Some of these estimators are designed to use a single low rank snapshot vector, while others employ multiple snapshots. This dissertation deals with both these cases in different contexts. Separable nonlinear least squares is a popular tool to extract parameter estimates from a single snapshot vector. Asymptotic statistical properties of the separable non-linear least squares estimates are explored in the first part of the thesis. The assumptions imposed on the noise process and the data model are general. Therefore, the results are useful in a wide range of applications. Sufficient conditions are established for consistency, asymptotic normality and statistical efficiency of the estimates. An expression for the asymptotic covariance matrix is derived and it is shown that the estimates are circular. The analysis is extended also to the constrained separable nonlinear least squares problems. Nonparametric estimation of the material functions from wave propagation experiments is the topic of the second part. This is a typical application where a single snapshot vector is employed. Numerical and statistical properties of the least squares algorithm are explored in this context. Boundary conditions in the experiments are used to achieve superior estimation performance. Subsequently, a subspace based estimation algorithm is proposed. The subspace algorithm is not only computationally efficient, but is also equivalent to the least squares method in accuracy. Estimation of the frequencies of multiple real valued sine waves is the topic in the third part, where multiple snapshots are employed. A new low rank signal model is introduced. Subsequently, an ESPRIT like method named R-Esprit and a weighted subspace fitting approach are developed based on the proposed model. When compared to ESPRIT, R-Esprit is not only computationally more economical but is also equivalent in performance. The weighted subspace fitting approach shows significant improvement in the resolution threshold. It is also robust to additive noise.

Separable least squares are generally written in the form ‖y−A(q)c ‖2 = min where minimization has to be carried out with respect to the parameters q and c. The latter enter linearly into the expression of the objective function and this leads to considerable simplications. These simplifications are not possible if the functional to be minimized is of the form σ‖y−Aj(q)c‖2 = min In this communication we modify previous methods, so that they can deal with the more general case (2). We also show that the statistical properties of both linear and nonlinear estimates can be evaluated according to a procedure that enables us to keep the two classes of parameters separate. An important application is examined and its numerical solution worked out in detail.