# Search Space Reduction for Localization and Tracking of an Acoustic Source
## 2 The Experiment
### The 2D Initial Guess  
Personal archival data with the site bathymetry in geographical coordinates were converted to UTM coordinates, as well as the VLA and stationary source GPS positions. To simplify the calculation of replicas, the obtained cartesian coordinates were further shifted in order to place the VLA at the origin of the bathymetry (see Figure 1); the expected range between the stationary source and the VLA range was calculated from these coordinates, providing the value \(r_{\mathrm{s}}=5836\) m. The source bearing relative to the VLA was found to be \(\phi_{\mathrm{s}}=93.3^{\circ}\). Combined errors of GPS positions and wind-induced source drifting provide an error in the source range of approximately 400 m and a source bearing between \(91^{\circ}\) and \(95^{\circ}\). From the description of experimental conditions, bearing estimates for the stationary and moving sources were expected to lie within this interval. The map shown in Figure 1 reveals a bathymetry in which depth increases mildly from right to left, with almost vertical isobaths; in particular, the isobath passing at the source slightly misses the VLA and gently deviates to the left in the region with \(Y<0\). The bottom model adopted considered a single layer over a half space (see Figure 2); this model was adopted from the literature (see [5; 17]). The corresponding properties are shown in Table 2. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Latitude (Degrees)** & **Longitude (Degrees)** \\ \hline Source & 4306.01 N & 1009.91 E \\ VLA & 4302.86 N & 1010.01 E \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Source ballast and VLA GPS positions. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Property** & **Value** & **Units** \\ \hline water depth & 128.9 & m \\ layer thickness & 3.3 & m \\ layer density \(\rho\) & 2.0 & g/cm\({}^{3}\) \\ layer initial compressional speed \(c_{p}\) & 1505 & m/s \\ layer final compressional speed \(c_{p}\) & 1556 & m/s \\ layer attenuation \(a_{p}\) & 0.11 & dB/\(\lambda\) \\ half space density \(\rho\) & 1.06 & g/cm\({}^{3}\) \\ half space compressional speed \(c_{p}\) & 1556 & m/s \\ half space attenuation \(a_{p}\) & 0.18 & dB/\(\lambda\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Bottom model properties. Several sound speed profiles (SSPs) are provided with the acoustic data; however, different trials of replica generation demonstrated that the only SSP that can provide consistent estimates of source position for the 2D initial guess is the one shown in Figure 3. This is somehow surprising in terms of the stationarity of sound speed over two days of transmissions, and this is an issue that deserves future discussions. The SSP has unusual features: above 60 m depth, it is almost constant, while in the interval from 60 to 80 m, it exhibits a strong thermocline, with a negative gradient; below 80 m depth, it decreases almost linearly. In terms of ray propagation, the SSP divides the water column into two different waveguides: for a source placed above 60 m, rays will bounce within the surface and the bottom, no matter what the launching angle is, while for a source placed below 60 m, rays with small launching angles will bounce on the bottom repeatedly, and steeper rays will \"escape\" the thermocline and bounce within the two boundaries. However, ray field predictions were not used in source localization due to the fine-scale irregularities of the SSP and because ray models cannot account for layer properties; replicas were instead calculated with the KRAKEN normal mode model, which provides rather smooth predictions of the modes (see Figure 4) and easily accommodates the different parameters of the bottom model. Figure 1: Bathymetry of the experimental site in cartesian coordinates, with the VLA (black diamond) placed at the origin; the black circle represents the stationary source position. Figure 2: Scheme of bottom properties.