# Shipborne GNSS-Determined Sea Surface Heights Using Geoid Model and Realistic Dynamic Topography
## 5 Derivation and Validation of Shipborne GNSS-Based Sea Surface Heights
### Reducing the Effects of Sea State Conditions
For comparison, the low-pass filter was also used on residuals (also estimated using Equation (2)) determined directly from the instantaneous SSH of  
Figure 10: Filtering window length dependency on GNSS sampling rate and vessel velocity, by assuming an optimal filtering window size of 53 measurements. Figure 9: Sum of absolute difference (SoAD) functions for the marine survey campaigns. Optimal filtering window sizes are shown with dashed vertical lines. individual antennas (i.e., instantaneous SSH from Equation (8)). The results of the C2 campaign before and after data filtering are shown in Figure 11. Notice how the unfiltered residuals of antennas A1 and A2 (at the vessel's bow) are more scattered than antennas A3 and A4 (and the joint solution), suggesting a dominating pitch motion at the vessel's bow and that the vessel is more stable near its mass center (cf. Figure 7). Such a revelation implies inferior results for the C4 campaign (recall that the center of mass solution could not be computed). After filtering, significant discrepancies could be detected between the center of mass and individual antenna solutions (Figure 11b). Residuals of the port side antennas generally appeared lower than starboard antennas' (a similar pattern can be observed for all other campaigns). The likely cause is the change in the vessel's general attitude. During total station and tape measurements in the harbor, the vessel was always tilted slightly to the right [23]. The vessel may correct its general attitude while in motion; thus, resulting in lower and higher than actual heights for port and starboard side antennas, respectively. Since the vessel rotates approximately around its mass center, the joint solution \(iSSH_{COM}^{Final}\) should consider such a motion. To further analyze the performance of conducted computations, the unfiltered and filtered residuals were compared (i.e., filtered results were subtracted from unfiltered). The statistics of their differences are summarized in Figure 12. The most significant differences were consistently detected for antennas A1 and A2, again suggesting dominating pitch motion at the vessel's bow. A reduced standard deviation was always (except for the C4 campaign, which showed no improvement) produced for the mass center solution. In contrast, the low-pass filter eliminated more noise from individual antenna solutions (i.e., resulting in greater differences between unfiltered and filtered residuals). It, hence, appears that the vessel's high-frequency attitude changes were indeed eliminated (or at the very least significantly reduced) in the \(iSSH_{COM}^{Final}\) (cf. Section 5.1). Figure 11: Residuals of the C2 campaign for antennas A1–A4 and the mass center solution (denoted CoM), (**a**) before and (**b**) after low-pass filtering. The described outcomes demonstrate the importance of proper planning for such marine GNSS surveys; the location of the antenna has a significant influence on data accuracy. Before validating this study's results, vessel sailing-related corrections must be estimated and removed from the filtered residuals. The following section describes their empirical derivation.