# Statistical Pass-By for Unattended Road Traffic Noise Measurement in an Urban Environment
## 2 Background  
In 2006, the Tuscany region planned the LEOPOLDO project with the intent to develop innovative noise mitigation techniques for action plans relating to road infrastructure to find the best surface criteria based on the surroundings of the laying and to develop measurement protocols useful for assessing road surface effectiveness and time stability in terms of both acoustical and safety characteristics. SPB-ISO and CPX were applied within the LEOPOLDO project, and improved protocols for measurements and for data postprocessing were developed [31; 32]. An improved version of SPB was developed (SPB-L) using a different noise metric than the original version. The SPB-L procedure was based on measuring the acoustical energy of the passing vehicle; it uses the Sound Exposure Level (SEL or L\({}_{\text{E}}\)), calculated according to the ISO 1996-1 [33], and the pass-by event is the signal part in which L\({}_{\text{Afmax}}\) exceeds the background noise by more than 10 dB(A), as defined in ISO/DIS 11819-1 [10]. A scientific debate was raised at that time [34; 35; 36; 37], and different metrics were proposed for SPB analysis, which led the LEOPOLDO project to adopt SEL instead of L\({}_{\text{Afmax}}\) as a metric in its SPB-L method. Later, the ROSATNE project [38] found good correlation between L\({}_{\text{Afmax}}\) and SEL. Although SEL is considered more sensitive to ground effects, it is still considered as a relevant option for helping the definition of common noise modeling methods [39]. The SPB-L followed the HARMONOISE [35] and IMAGINE [36] projects, which introduced a second measurement position placed at 3.0 m height and 7.5 m distance from the center of the road lane (SPB-HI). This improved the evaluation of the influence of the local context by avoiding the roadside ground influence that was not negligible with only the 1.2 m height position. Thus, SPB-L measurements include two microphone heights. Thus, the statistical sample of many single passages constitutes the dataset for the logarithmic regression (Equation (1)) between the measured speed \(v\) and the \(SEL\), which estimates the level at the reference speed \(v_{0}\), in accordance with SPB-HI. \[SEL=a+b\cdot log\left(\frac{v}{v_{0}}\right) \tag{1}\]  
where \(a\) is the \(SEL\) at reference speed (typically 50 km/h), and \(b\) is a speed-related correction. A further improvement of SPB-L was the introduction of the use of statistical data binning since the SPB-HI procedure fails when speed data are collected around a single value, such as the speed limit. In fact, the variability due to driver behavior and to vehicle characteristics dominates when the speeds are almost the same. Data then have a cloud-like shape, and those falling outside the cloud influence the fit algorithm. This influence is avoided through statistical data binning applied to the whole dataset and a minimum chi-square fit of central values with their uncertainties. In more detail, data are grouped in velocity classes, or bins, about 10 km/h in width. The actual width is chosen to minimize the total chi-square of the final fit. The mean and standard deviations of data in each class are computed with the hypothesis of a Poissonian distribution of the vehicles data, with each class represented by the triplet: central velocity of the class and the mean and standard deviation of the SEL data contained in each class. These triplets are used as inputs in the best fit between SEL and speed. In this way, the information of data spread out, and the numerousness in each speed bin is taken into account by means of the uncertainty associated with the central values. Within the NEREiDE project, a further improvement of SPB was looked for in order to simplify SPB measurement and analysis protocol, especially sparing man time on site.