Thesis - Instituto de Telecomunicações

72 CHAPTER 4. SIGNAL PROCESSING AND FEATURE EXTRACTIONthat will be used in the definition of the following EDA models.Equation 4.21 constitutes the base model of an isolated SCR event, presenting 4 parameters:the rise time t r , the decay time, t d , a gain g and the onset time, t o .The total EDA is modeled by adding to the previous SCR, the skin conductance level(SCL), modeled by a constant and a negative exponential (representing signal decay), leadingto the function f m :f m (t) =a exp(−t/t d )+f s (t)+c. (4.23)The situation of two overlapping SCR events is modeled by an 8-parameter function f g ,defined byf g (t) =a exp(−t/t d )+f s1 (t)+f s2 (t)+c. (4.24)In this final model, it is assumed that all SCR events share the same decay (t d ), and risetime (t r ) parameter values. Two events will differ in the values taken for the amplitude(gains g 1 and g 2 ) and onset time (t o1 and t o2 ) parameters. The distinctive Skin ConductanceLevel (SCL) model parameters are a constant level (c), and a gain (a) affecting a decayingexponential, since the associated decay parameter t d is also assumed to be the same of theSCR events.Using the complete model in equation 4.24, the detection and quantification of pairs ofoverlapping events is accomplished by means of an optimization process that fit the modelparameters to the observed data. The fragility of this model is in the selection of the initialparameters for the optimization procedure. It has been shown to be very difficult to providea good initial approximation that guarantees the convergence of the optimization process[6]. The model also lacks an extensive validation. While the base single event model inequation 4.23 was tested in 60 SCR segments, the authors stated [146] that the completemodel was only fitted to three double SCR responses.This proposal showed a method to solve the overlapping of SCR events, but the intrinsicproblems of the optimization task were not completely solved. Parameter initializationproved to be crucial to the success in obtaining a good fit of the model, an issue notdiscussed in the work in [146].Bi-exponential Model Also motivated by the short interstimulus-interval that provokesoverlapping skin conductance responses, Alexander et al. [6] proposed a bi-exponential