## 3 Results
### From Measurements to Continuous and Retrospective Perceived Pleasantness  
#### 3.2.1 Continuous Sound Pleasantness Estimation Based on Noise Level Time Series  
Section 3.1 demonstrated the possibility of relating the global sound pleasantness of a 3-min walking trip, to its perceived pleasantness time series. Thus, relating the perceived continuous sound pleasantness values to physical noise indicators, is a required intermediate step for proposing an estimate of the global sound pleasantness based on noise level time series. This section attempts to develop such relations, from the corpus of the 10 audiovisual sequences. As a first step, the instantaneous sound pleasantness \(P\), assessed at time step \(t\), is estimated, based on a constant aggregation of the noise levels measured in the recent past. The modelling calls for two parameters, namely the response time \(rt\), and the integration time \(it\). The response time describes the delay between the noise event and its assessment by the participant. It corresponds to the time needed to detect the sound, then to understand and assess it in terms of pleasantness, and finally to move the cursor to the targeted point on the screen. The integration time describes the signal duration taken into account by the participant, for the instantaneous pleasantness assessment. As a result, \(P(t)\) can be estimated using the following formula: \(P(t)=f(t\text{-}rt\text{-}it\text{:}t\text{-}rt)\), where \(f\) is a time series of the noise levels between \(t\text{-}rt\text{-}it\) and \(t\text{-}rt\). Then, the modelling consists of finding the function \(f\), and the \(rt\) and \(it\) values, which maximize the correlation between the estimated and the actual \(P(t)\) values. Figure 6 presents the correlations, averaged over the 10 sequences, between all the instantaneous 125 ms pleasantness rates and the calculated \(f\) function, for different \(rt\) and \(it\) values, and considering the function \(f\) and the usual noise indicators \(L_{50}\), \(L_{90}\), \(L_{10}\), and \(L_{\rm eq}\). The presented correlation is calculated over 1000 observations (from the 3-min sequences sampled at 125 ms, but subtracting the earliest 400 values for integration purposes). The four noise indicators result in similar correlations, although correlations when using \(L_{90}\) are slightly less significant. The correlation curves simultaneously describe the influence of the two parameters, \(rt\) and \(it\). The best couples \(\{it;rt\}\) range between 3 and 10 s for \(it\), and between 0 and 2 s for \(rt\). The maximum correlation found, 0.84, is obtained for the couple \(\{6;0\}\) and the \(L_{\rm eq}\) function. Thus, the resulting integration time, also called the \"psychological or perceptual present\" in [37], is about 6 s. Nevertheless, it is not possible to dissociate the couple \(\{it;rt\}\), as the integration time includes _de facto_ a part of the reaction time. Using the same methodology proposed by [PERSON] and [PERSON] [37], the reaction time is defined for a null integration time, which corresponds to approximatively 2 s for this experiment (couple \(\{0;2\}\)). These values are slightly higher than the durations found in the literature, for the continuous assessment of sound levels. For example, the best couples \(\{it;rt\}\) found in [37] for perceived sound level assessment are \(\{2.5;0\}\) and \(\{0;1\}\). This might be due to the higher complexity of an appreciation task. To develop this analysis, the SIMPLE model presented in the previous section is calibrated for determining the weighting of the sound level time series. The parameter \(rt\) was added to the original ones, in order to introduce the reaction time into the SIMPLE model, adding a delay to the original weighting function. The SIMPLE parameters are optimized over the last 30 s, in order to obtain the best estimation of the instantaneous pleasantness, according to the sound level.