## 6 Discussion  
The proposed algorithm considers three unknown parameters: the group velocity and the in-plane coordinates of the AE sources. The method chosen to define the starting value of the group velocity is performed by the Monte Carlo simulation. The algorithm based on EKF allows the convergence between the initial values as well as the differences in time of arrival of the signals detected by the different sensors. This approach represents an advantage compared to the one proposed in a classical AE system. In the latter, damage or impact location is based on the triangulation method, which involves the time-of-arrival (TOA) taken at multiple receiving points. The classical AE system gives very good results when the wave velocity (\(V_{g}\)) of the considered Lamb wave and the TOA are known. However, TOA and wave velocity are two uncertain parameters. In general, uncertainties can be caused by random and systematic errors. The random errors are caused by unknown and unpredictable changes in the TOA measurements, including instrumentation noise, temperature changes etc. [14; 15; 16; 17; 18; 19]. Systematic errors are mostly caused by the digital signal processing technique used for analyzing the AE waveforms [20]. In real operational and environmental conditions (noise, stress state, temperature changes, different impact scenarios, etc. ), measurement errors are known to influence the propagating mode in terms of velocity and attenuation. In the case of our experiment, the attenuation can be considered as unchanged. However, the group velocity will change especially as a function of the stress conditions to which the material is subjected (i.e., acoustoelastic effect). If the velocity changes, the classical AE system will not be able to perform an automatic update. The positions of AE sources indicated by the classical AE system will be therefore erroneous. In that sense, the method proposed in this contribution comes to complete this insufficiency. The spatial convergence of the proposed algorithm, shown in Figure 7, is performed in just six iterations. Locations are determined with a good accuracy for PLB performed away from the edges of the specimen (i.e., less than 4% in both \(x\) and \(y\) coordinates). In such a case, the maximum error to estimate the coordinates of the different locations did not exceed ~5 mm. We also performed PLB measurements close to the edges of the specimen and outside the domain defined by the four sensors. In this case, signals are naturally more affected by reflections from the lateral edges. The accuracy of the location and the maximum error does not exceed ~15 mm (Figure 7). The case where the source location is not a priori known is not very different from the case studied during the mechanical test. Indeed, it is expected from a material such as aluminum, that AE originates both from fracture of particles and from dislocation related sources. The creation and propagation of a crack in metals is accompanied by plastic deformation at the crack tip [68]. It was also found that the maximum plastic zone is situated in the interior but closer to the surface than to the mid plane [69; 70; 71; 72; 73; 74; 75]. Therefore, the plastic zone, which is also a source of AE signals, is surrounding the propagating crack and contributes significantly to the scattering of locations, as can be seen in Figure 13.  
Finally, we note that in real experimental conditions the presence of noise and multiple crack detection are inevitable. The use of time filters namely the hit definition time (HDT), the hit lockout time (HLT), and the peak definition time (PDT), helps to separate AE signals and significantly limits their overlap. In our tensile experiments, we note that despite the calibration of the time filters, some AE hits still overlap but their number remains limited (less than 10%). The presence of noise requires some considerations. In general, threshold should be ~4 dB above noise level. If the threshold is high, a significant loss of AE signals might occur.