Precise Vertical Position Fixing

Recent development of a 3-dimensional precise positioning technique by Kinematic GPS (KGPS) makes it possible to realise accurate vertical positioning to several centimetres, even in the sea. But observed vertical positioning data in the field includes various disturbances such as ship pitch and roll, squat, and tidal fluctuation, which have to be removed for accurate positioning. The movement of the ship was therefore observed using inertial and GPS-integrated gyroscope, and the stand and squat by three KGPS sets at the stem, centre and stern of the ship. Correcting these disturbances to the raw data of vertical position by KGPS, obtained sea-level heights were considered almost stationary to exclude time changes. In order to evaluate its accuracy, the corrected data taken at the same points of the survey and cross-check lines were compared, resulting in accuracy estimated at about 5cm, enough to fix sea-level height for practical use.

Sea-level height by KGPS is defined according to the WGS84 Reference Ellipsoid (RELP) and chart depths are referred to the Chart Datum Level (CDL). If we have the CDL distribution model referred to the same RELP, the chart depth will be obtained directly from the sounding depth and the sea-level height, without tidal correction. Thus the vertical positioning by KGPS and CDL model fixed on the same RELP WGS84 are expected to provide a breakthrough in hydrographic survey in the near future. Some attempts in this direction by the Hydrographic and Oceanographic Department of Japan are introduced here.

KGPS Field Experiments
Using Survey Vessel Hamashio (length 21m, 27 tonnage) of the 3rd Regional Japan Coast Guard Headquarters, a field experiment in vertical positioning by KGPS was carried out in Tokyo Bay (Figure 1). Survey lines of East-West and cross-check lines of North-South were set in the inner area of the bay adjacent to the tide station, which was used for monitoring the tidal change of sea-level. The vessel was navigated along the survey lines at constant speed, excepting some acceleration at the change of lines. Data of KGPS heights was sampled at 0.5-second intervals (results are shown in Figure 2) with ship speed and sea level observed at the tide station. KGPS height is apparently influenced by short periods of disturbance due to rolling of the ship, moderate sea-level change by tide and step-like change due to ship speed change.

Correcting KGPS Height

• Influence of ship movement:
  KGPS height data was influenced by short-period disturbance due to the roll, pitch and heave of the ship and these amplitudes sometimes reached more than 1m, depending on sea conditions. Therefore the roll, pitch and heave were detected using integrated inertia and GPS gyroscope (POS/MV) to correct KGPS heights; it was found that the disturbance was reduced to less than half by this means.
  
• Change of the stand and squat of SV due to the ship speed:
  The step-like change of heights shown in Figure 2 is definitely correlated to change of ship speed. Using three KGPS sets at the stem, centre and stern of the SV respectively, their heights were measured under the condition of various ship speeds, as shown in Figure 3. Getting up speed from a rest to 8 knots, the SV gradually increased squat, keeping its stand, which subsidence reached about 5cm at 8 knots. At the speed over than 10 knots its stand changed significantly, up at the stem and hugely down at the stern.

Tidal Change
Subsidence at the stern reached more than 30cm at 13 knots. In the precise fixing of the vertical position, we have to correct the influences of stand and squat to the KGPS height data. In the field experiments, in order to reduce these influences we tried to keep ship speed constant at 6 knots, except at the change of survey line.
The test field was located in the innermost area of Tokyo Bay, as shown in Figure 1, where tidal current was weak. Therefore it is considered that tidal characteristics are not so varied around the field. As shown in Figure 2, moderate fluctuation in KGPS heights was definitely correlated with the observed tidal change. KGPS heights were then corrected with the data observed at the tide station.

KGPS Heights and Mean Sea Level
Since short-period disturbance from ship movement, subsidence due to squat and stand and sea-level change by tide were almost removed from the measured KGPS heights, the residual KGPS heights were considered to include almost no temporal changes; the residual heights were considered to reflect the spatial distribution of sea level. In other words, the residual heights indicate the data traced instantaneous mean sea level referred to the RELP. That is to say in exact terms that the fluctuation of zigzag as shown in Figure 4 means the up and down of the ship navigating along the paths on the slope of the mean sea-level, inclined relatively to RELP as shown in Figure 5. Actually, the residual KGPS heights coincided with the geoid model (GEOID2000) around Japan made by the Geographic Survey Institute, and their difference was not more than several cm as shown in Figure 4.

KGPS Heights Accuracy
Accuracy of vertical positioning of KGPS height was evaluated through five field experiments, including that in Tokyo Bay. The residual KGPS heights that removed temporal change should take same value at the cross-point, even along the survey line or along the check line. Comparing their difference at 772 cross points, the average of difference was evaluated to be 5.1cm and root mean square was 4.0cm. Considering that ordinary hydrographic surveys are carried out in the order of resolution of decimetres, this KGPS height accuracy is enough to apply.

Summary and the Future
In the traditional hydrographic survey, instantaneous depth of the sea bottom is measured by an echo sounder relatively to the instantaneous Sea Surface Level (SSL). To convert to the charted depth, it is necessary for the sounding depth to correct the tide using tidal data and to fix on Chart Datum Level (CDL). The tidal correction is based on the assumption that the relation of SSL and CDL at the survey site are the same as that at the tide station, and both levels are horizontal to each other. However, RELP is not always horizontal and is inclined to the SSL or CDL, as shown in Figures 4 and 5. Trying to use the KGPS heights for vertical fixing of SSL instead of tide gauge, we have not to apply the relation of the CDL and RELP at a site to that at another site. Even if the sea bottom height above RELP is known at the site, in order to get the charted depth referred to CDL, CDL height above RELP should be prescribed just at that site. CDL is defined as the level surface of Z0 below the Mean Sea Level (MSL), and Z0 is separately given from the tidal observation or tidal model. It may be concluded that a final need to apply KGPS heights for hydrographic surveys is clear definition of MSL height distribution above RELP.
The Hydrographic and Oceanographic Department of Japan recently tried to make such MSL and CDL height distribution in coastal waters, corresponding with the development of vertical position fixing by KGPS as mentioned here. Figure 6 is one example of such trials, a CDL heights distribution in Seto-Naikai by Yabuki et al. (2002, Japan Hydrographic Association), which is inclined more than 7m in the distance of 350 km from east to west. As the vertical position fixing by KGPS was developed fairly well and validated through field experiments as described above, it is necessary to instil more confidence regarding MSL and CDL height distributions through further field experiments.
If the MSL and CDL heights distribution model is completed, vertical position fixing by KGPS will not only cut down the tidal correction in hydrographic survey but also realise a continuous ground survey consistent from land height to sea-bottom depth using a reference ellipsoid. Thus vertical position fixing by KGPS and a reliable MSL and CDL distribution model are expected to represent a breakthrough in various directions such as coastal engineering and navigation in the near future.