## 1 Introduction
In Reference [14], the authors investigated for the first time the application of ATI for the estimation of ocean currents. Data have been acquired by the shuttle radar topography mission (SRTM), which used an auxiliary antenna yielding a baseline aligned with the azimuth direction of 7 m. Unfortunately, the ATI configuration requires the use of multiple receivers and it is clear that, in order to obtain high sensitivity in estimating low-rate velocities, it is necessary to design relatively long baseline ATI geometries. However, there are no satellite systems configured in this way and therefore it is necessary to identify other solutions. Additionally, a common issue for techniques based on interferometric SAR is the dependency of the results on the quality of the image pair registration. Interferogram formation requires images to be co-registered with an accuracy finer than a few tenths of a resolution cell to avoid significant loss of phase coherence. For InSAR products co-registration, a 2-D polynomial of low order is usually chosen as a warp function, and the polynomial parameters are estimated through least squares fit from the shifts measured on image windows [15]. A direct consequence of accurate co-registration is the unlocking of the use of pixel tracking techniques. The use of pixel-tracking has proved to be effective for the precise space offset measurements of pixels located on co-registered sets of SAR images observing the same scenes by long temporal series. To this end, it is possible to process a couple of along-track interferometry single-look complex (SLC) SAR images observing the same scene. Specifically, the images must be formed in a short time interval, varying from some millisecondsto a few seconds. The phase differences between all range-azimuth resolution cells composing the two images are proportional to the Doppler shift of the backscattered signal. This technique has shown good potential for applications such as monitoring glacier movements, volcanic activities and co-seismic tears in the solid earth resulting from severe earthquakes, addressing some of the limitations of conventional differential InSAR (DInSAR) techniques, particularly their sparse coverage and the impact of highly vegetated areas [16]. Similar techniques have also been applied in low resolution SAR imagery, measuring large Earth deformations [17; 18] and recently it was found that pixel tracking is also suitable for micro-Doppler estimation of maritime targets [19; 20]. In this paper, we introduce a pixel tracking technique based on the localized spectral analysis with the objective to track in time the double-bounce scattering effect in order to measure the height of rivers. To achieve this objective, the proposed technique exploits the measurement of the distance between bridges or other man-made objects on the embankments. A necessary condition is that the structures are perpendicular to the slant-range direction. The height estimation is obtained by measuring the cross-slant-range distance between the edge of the structure and the echo of second bounce reflected by the river surface. This physical phenomenon is tracked over time in order to observe the trend of variation of the water level. The applicability of this method is supported by the fact that the double bounce echoes can be easily detected thanks to the shading effect generated by the bridge infrastructure. This echo is detected in the range cells immediately contiguous to those containing the bridge. The time tracking of the double-bounce echo shift is possible because in the instants of radar observation the river surface is operating as a mirror at variable distance. This distance is proportional to the height variation of the river's water surface. The echo space-time shift is due to the particular geometric SAR configuration where the images are observed in slant coordinates. In order to proceed with the estimation of the hydrometric levels it is therefore essential to develop a reliable tracking algorithm.